The modern orthopaedics frequently uses the total hip replacement in the artificial hip joint. The wear in this joint requires a re-replacement of hip joints because it is under the severe load and friction conditions. To solve these problems the previous studies have been mainly focussed on the development of new materials. The research of new materials, however, needs much time and effort since it should be experimented for its bio-compatibility, friction, and wear characteristics. To reduce the work, in this study, the finite element analysis is applied to find new combinations of bio-materials in the total hip replacement which has the excellent contact characteristics. A non-linear FEM program MARC with 5-node axisymmetric element was used for analyzing the contact stresses between the hip joints. The computed results show that in case of acetabulum UHMWP has good characteristics, in femoral head, $Al_2O_3$, and in stem, Ti6Al4V.