Solids are generally defined as "incompressible," but it is actually possible to compress some to a very small degree. However, it is difficult, and the solids' capacity to be compressed is limited as their particles are already close together and have relatively little room to move.
Each solid material has its own varying elastic properties, but solids generally break or deform when enough pressure is applied. Any room for compression is so insignificant that entry-level science textbooks and materials tend to summarize them as "incompressible" for simplicity. Two popular examples of compression of a solid are graphite and diamonds, which begin as carbon that has so much pressure exerted on it that the atoms rearrange.