The paper deals with the problems of ceramic head of hip joint endoprosthesis destructions, and with assessing the impact of shape deflections of conical surfaces on the probability of this failure. Concerned are shape deflections from the ideal conical surfaces of the stem and the head of the endoprosthesis, which - when the head is put on the stem and the endoprosthesis loaded - form a contact configuration. The shape deflections may be modelled at the macro-level - this concerns model shape inaccuracies such as deflection from the nominal degree of taper, ovality, and their combination, or, possibly, at the micro-level - when the stochastic distribution of unevenness on the contact areas is respected. The problem of stress in ceramic heads was solved using the algorithm of the finite element metod for spatial contact tasks, and the Weibull probability model was used for solving the problem of head cohesion failure probability. In the paper are presented and analysed the results of solution of the micro-level shape deflections, obtained from measurements made on the cones of stems and heads.