According to the standard surgical protocols, the press fit is obtained inserting an implant in a drilled hole that is provided with a lower diameter. In this way, it is induced a relevant strain state in the peri-implant bone that favors the primary stability of the implant. Experimental evaluation of this phenomenon is very difficult and does not offer a complete set of information. A numerical analysis is adopted to describe the mechanical phenomena occurring in the peri-implant tissue. At this purpose, suitable constitutive models are adopted for the bone tissue for the evaluation of plastic and viscous effects caused by the real strain field induced. Specific numerical procedures are developed to model the press fit action of an implant against the surrounding bone tissue and the subsequent viscoelastoplastic effects determined. The results of the numerical analysis make it possible to estimate the deformation caused by the insertion of the implant and the evolutionary trend after insertion by considering the inelastic time-dependent behavior of bone tissue in peri-implant region. According to the viscous characteristic of the bone tissue, the numerical analyses show a stress relaxation in the order of 30% around the implant.