here's a some images showing the result of cutting foam rubber. The material normally used for upholstery and matrasses.
You can get this material as a leftover material at "ABC schuimplastic huis" in Amsterdam, when they make mattrasses they cut it out of an enormous block of foamrubber at least a couple cubic meters . These thin mats are the cut offs from the bigger pieces. The material is not always consistant in thickness but very affordable this way. It's super flexible and could be used for lots of applications in textiles.
I use the material to cut geometric patterns which I will then further integrate into upholstery-like materials.
The material is about 1 cm thick and is very lightweight. I use fairly high power combined with low speed. power :80 / speed: 1.8. Still it goes quite fast in my opinion. With these settings you just don't cut al the way through, which is convenient because everything stays together and you don't end up with loads of small pieces you have to clean up. then afterwards you easily tear out the shapes without damaging the material.
Using slower speed gives you an all-the-way-through cut but also tends to taper the foam. This is because the material on top is exposed longer to the laser and this way melts/shrinks. So the cut on top of the material is wider than the cut on the bottom.
these are my first findings after a couple of tests. But overal it's a nice and easy material to work with.