Numerical modeling of the insertion of a cylindrical indenter with various forms of the top into biological tissue is carried out in the case of finite deformations and the presence of friction between the cylindrical surface and the tissue. Soft biological tissue or its phantom is modeled by a two-layer elastic material, the thickness of the surface layer and the elastic properties of the layers vary. Fracture of the material of the surface layer and crack growth in the depth of the sample are considered. The analysis of emerging internal stresses is presented.