The article has been devoted to issues connected with the alloplasty and hip joint endoprostheses, that elements are being developed, which is supported by strength, tribological tests on used biomaterials, incl. polyethylene or computer modelling based on e.g. finite element method (FEM). In this paper, the results of research on the impact of the material articulations of the system head – acetabular and friction conditions on strength parameters of polyethylene components in the hip joint endoprosthesis. Numerical analysis of this friction node was carried out, using the ADINA System computer program and the simulations were performed at various friction conditions for metal/ polyethylene and ceramic/ polyethylene articulations with various UHMWPE modifications. The simulations results have shown the influence of tested material associations and friction conditions on parameters related to the strength of polyethylene cups, i.e. their displacements, stresses and deformations.