I’m not a biologist, but if I understand your question correctly, you are basically looking for land-based invertebrates that also lack a hardened exoskeleton (like insects). This would basically consist of small, soft animals like snails, slugs, leeches, tardigrades, and tons of different types of worms.

The reason that you don’t see large examples of this in land-dwelling creatures is that skeletons or exoskeletons become way more necessary without a medium like the water in the ocean to help support a body. The rigid structure provides an attachment point for musculature to create the mechanical levers we use to manipulate our limbs.

Would you please elaborate on your question? What do you mean by an elastic skeletal system?

Can you give an example, even if fictional?