This work presents a comparative study on the bioresorption of samples based on natural biopolymers, such as polyhydroxybutyrate, polylactide, polycaprolactone, and chitosan, in living systems and an evaluation of the tissue response to these samples. A histological examination of the polylactide-containing tissue samples revealed that the material possesses good supporting functions for connective, bone, and granulation tissues and causes no pronounced inflammatory infiltration with lymphocytes, neutrophils, and giants cells of foreign bodies. The resorption of the material proceeds slowly, and metabolites released during the resorption have no negative effect on the reparative osteogenesis. These materials seem to be quite promising in veterinary medicine.