The two Earth layers made of solid material that does not flow are the crust and the inner core.

Here's why:

* Crust: The outermost layer of the Earth, the crust is relatively thin and composed of solid rock.

* Inner Core: Despite immense pressure and heat, the inner core is solid due to the extreme pressure. While the material is iron and nickel, the pressure is so high that the atoms are tightly packed, preventing them from flowing.

Let me know if you'd like more information on any of these layers!