The paper presents mathematic-statistic methods defining the influence of stress on ceramic elements’ durability of hip and knee joints endoprostheses. The tests were conducted with Finite Elements Method in the ADINA System. The obtained results state the influence of load on the values of durability and stress, that get formed in ceramic parts of joints, and help to detect and solve technical problems and thus, counteract the subsequent effects resulting from premature wear of endoprosthesis elements. The paper emphasizes necessity of discovering new materials, that will be bio-compliant and wear resistant. Although ceramic materials like Al2O3, ZrO2, are brittle and less resistant to load than metallic implants, their improving mechanical parameters (excellent tribological properties), make them becoming new standard in biomaterials for clinical use. That opens new possibilities especially for hip or knee joints alloplasty.