The purpose of this study is to investigate the effect of the ball-cone contact interface variation on the ceramic ball stress which is the dominant factor of the design of the moldular artificial hip joint. A contact stress analysis problem is formulated using the optimization principle and finite element analysis technique on the ball-cone system of three dimensional axi-symmetrical model, Numerical procedure is employed to get the solution for varying angles of cones and angular mismatches between the ball and cone interfaces. There is a fair amount of friction in the interface and included in the analysis model.