We consider typical features in application of computer modeling methods to design implants of optimal shape and composition. Nanostructural medical grade titanium and bioactive ceramic components, synthesized on the basis of hydroxyapatite, are used as material for joint endoprostheses. Studies are based on the assumption that compact bone is an elastic, orthotropic, porous material. The presence of friction and heating in the contact regions is taken into account. The problem is considered in a thermoelastic formulation. The solution of this problem will make it possible to optimize both the geometric characteristics of implants and their composition.