For below your material and on top of the mat, you can place just about anything that is ~ as thick as the punch tool itself. For example, craft foam (fun foam) will work or even a spongy type mouse pad. If you’re asking what kinds of materials to punch for a design, then I recommend vellum or cardstock or even paper. There’s info about using the punch tool in your KNK user manual that you might want to read. You don’t mention which KNK model or software you own, so I cannot direct you to the specific section, but every KNK user manual has info on the punch tool in one of the later accessory chapters.