Probably because it's an alpha version, with lots of unfixed bugs and such.
I found a way to "save" models! Simply click "Show XML" and Copy-And-Paste the contents into a file. To "load" the model, Copy-And-Paste the contents of the file back into the box and click "Load". Your model appears, again.
Here is a demo model: a big triangle-structure that I created in 3 minutes using Copy, Paste, and Fuse.
<object type="com.sodaplay.soda.constructor2.ConstructorApplication"> <thingspace /> <field name="model"> <object type="com.sodaplay.soda.constructor2.simulator.Model"> <field name="autoReverse"> <boolean>true</boolean> </field> <field name="comment"> <string /> </field> <field name="friction"> <double>0.2</double> </field> <field name="gravity"> <double>0.0</double> </field> <field name="gravityDirection"> <int>1</int> </field> <field name="height"> <int>430</int> </field> <field name="nodes"> <list class="java.util.Vector"> <object id="object25-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>1.4135885768740142E-5</double> </field> <field name="vy"> <double>1.516033927044247E-5</double> </field> <field name="x"> <double>212.50089106336463</double> </field> <field name="y"> <double>248.64175068366825</double> </field> </object> <object id="object26-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>1.1462816775616116E-7</double> </field> <field name="vy"> <double>8.802840272527769E-5</double> </field> <field name="x"> <double>213.60604022413992</double> </field> <field name="y"> <double>308.63162139975395</double> </field> </object> <object id="object27-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>-5.233129811071213E-7</double> </field> <field name="vy"> <double>1.7726130457441365E-5</double> </field> <field name="x"> <double>264.9026200942557</double> </field> <field name="y"> <double>277.86598645198774</double> </field> </object> <object id="object28-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>-2.0776143320504528E-5</double> </field> <field name="vy"> <double>7.234279106542753E-5</double> </field> <field name="x"> <double>265.58068317608536</double> </field> <field name="y"> <double>337.8622203040816</double> </field> </object> <object id="object29-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>3.3300170429783624E-5</double> </field> <field name="vy"> <double>1.5544029296335094E-4</double> </field> <field name="x"> <double>316.98971166591804</double> </field> <field name="y"> <double>307.64764782413255</double> </field> </object> <object id="object30-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>-7.271746149456746E-5</double> </field> <field name="vy"> <double>-5.763832651038361E-5</double> </field> <field name="x"> <double>316.2039491432729</double> </field> <field name="y"> <double>247.4694638265496</double> </field> </object> <object id="object31-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>-4.980046716438181E-5</double> </field> <field name="vy"> <double>-6.46686460396227E-5</double> </field> <field name="x"> <double>211.6092414610463</double> </field> <field name="y"> <double>188.6483026586512</double> </field> </object> <object id="object32-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>-1.7262329779610397E-6</double> </field> <field name="vy"> <double>-2.944248737752342E-5</double> </field> <field name="x"> <double>263.9066352024016</double> </field> <field name="y"> <double>218.05890478621077</double> </field> </object> <object id="object33-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>3.779121245630539E-5</double> </field> <field name="vy"> <double>-5.352300083042358E-5</double> </field> <field name="x"> <double>263.3363744740685</double> </field> <field name="y"> <double>158.24625958154073</double> </field> </object> <object id="object34-com.sodaplay.soda.constructor2.simulator.Mass" type="com.sodaplay.soda.constructor2.simulator.Mass"> <field name="vx"> <double>6.008090386759868E-5</double> </field> <field name="vy"> <double>-1.4396962981305105E-4</double> </field> <field name="x"> <double>315.52879889993415</double> </field> <field name="y"> <double>187.84264008514722</double> </field> </object> </list> </field> <field name="springs"> <list class="java.util.Vector"> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object26-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object26-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object31-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object31-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object25-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object26-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object28-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object26-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object28-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object30-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object30-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object28-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object27-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object29-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object28-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object29-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object29-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object30-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.18320732371843</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object30-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object34-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object30-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object34-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object31-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object31-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object33-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>60.0</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref refid="object32-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="b"> <ref refid="object33-com.sodaplay.soda.constructor2.simulator.Mass" /> </field> <field name="restLength"> <double>59.630537892348144</double> </field> </object> <object type="com.sodaplay.soda.constructor2.simulator.Spring"> <field name="a"> <ref 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