The paper presents the numerical analysis of stress and strain occurring in the most wearable parts of hip and knee joints endoprostheses. The complexity of the processes taking place in both, natural and artificial joints, makes it necessary to conduct the analysis on the 3D model based on already existing mathematical models. Most of the mechanical failures in alloplasty are caused by material fatigue. To cut down the risk of it, we can either increase the fatigue resistance of the material or decrease the load strain. It is extremelly important to indicate the areas where damage or premature wear may occur. The Finite Elements Method makes it possible to calculate the stress and strain in particular elements of the tested models. All presented numerical calculations define quality conclusions concerning the influence of some parameters of endoprostheses on the values of stress and strain that are formed in polyethylene parts of endoprotheses of hip and knee joints. The obtained results help to reveal “weak points” in examined models and thus, counteract the subsequent effects resulting from premature wear of endoprosthesis elements.  The numerical analysis was performed basing on the finite elements method using Autodesk Simulation Mechanical 2016 software and the ADINA 7.5.1.