The Elbsandsteingebirge (Elbe Sandstone Mountains), as the name says, is a series of sandstone mountains. The rock is eroded forming vertical cliff faces, towers, and escarpments. This landscape is similar to canyonlands or badlands in the United States, although probably smaller in extent and less bombastic. The sandstone is a Cretaceous sandstone form in a shallow sea. Quartz rich sand with a lot of iron oxide in the matrix, which explains the red colour.
There are massive layers of hard sandstone with thin layers of siltstone inbetween. Those layers are often impermeable, so water is dammed and flows to the cliff face where it forms springs. The silt layers are both weaker and also subject to heavier erosion, because of the water. The result is the formation of horizontal wedges and even caves, until the rock above breaks down. The talus is continually conveyed to the sea by the Elbe river below. This continuous process sharpens the edge and keeps the cliff face vertical. Or in other terms: the erosional processes reached an equilibrium at which the formation of cliffs and towers is supported instead of them being eroded.
As we already mentioned, there are horizontal caves formed by the erosion along soft layers in the sandstone. They often have a small spring inside caused by the impermeable silt. But while they are wide, they are not very deep and the ceiling is often low, so it is necessary to crawl.
Another common type of caves in the area are tectonic caves, both fissure and talus caves. Both cave types are basically formed by movements of the rock. Fissure caves are the result of movements of the huge rocks. They may be open like the Himmelsleiter (Stairway to Heaven) or real caves. Talus caves are fissures inside the talus heaps at the foot of the cliffs.
The area, although rich in caves, is not a karst area. The caves are mostly very small. Some geologists tend to describe it as a sandstone karst area, which is actually an oxymoron. However, the discussion is mainly on the terminology, and not on the processes involved in the formation of the caves.