Polyethylene parts of endoprosthesis are the weakest parts of each medical implant. They can be worn out within several years. During this period, a patient can enjoy good physical efficiency until the wear of polyethylene part limits his/her mobility. Then the reoperation is necessary and positioning of all parts of endoprosthesis has an effect on future patient's mobility and durability of implant. Elements of endoprosthesis during exploitation are heavily loaded both by normal and tangential forces and moments. In this paper, the dependence of wear of polyethylene cup on its positioning in pelvis is the major problem. Wear of the cup is determined by two measures: the depth and volume of a material rubbed off from the contact surface. The sensitivity of the depth of rubbing off is evaluated relative to two angles of anteversion and abduction, and radii of the cup. Numerical results are obtained by using Abaqus FE system with data related to patient's activity identified on the basis of medical reports.