The initial stability of the cementless acetabular cup significantly affects the outcome of surgery for total hip replacement. Although it is essential to minimize the relative displacement between the pelvis and metal, few previous studies have addressed this issue. This study investigated the effects of varying the sizes of acetabular components on the stability. Eighty-one finite element models of total acetabular replacements with various configurations were created in the finite element package ANSYS. The following three size parameters and one fixation parameter were investigated: femoral head diameter (26, 28, and 30 mm), polyethylene liner thickness (9, 10, and 11 mm), metal cup thickness (2, 3, and 4 mm), and number of fixation screws (one, two, and three). In all of these models, one-leg stance loading was applied at the center of the femoral head, and the boundary condition consisted of immobile screw holes. The peak displacement at the cup exterior surface was used to evaluate the stability. The simulations indicated that the peak displacement was decreased by increasing the cup thickness, decreasing the polyethylene liner, and decreasing the femoral head size. The mechanisms affecting the stability were the structural stiffness and moment arm (effect distance between the loaded head center and the fixation screws). Increasing the cup thickness had a major impact on the structural stiffness and a minor effect on the moment arm, thereby decreasing the cup displacement. On the other hand increasing the head size or linear thickness had a larger impact on moment arm and a smaller effect on structural stiffness, thereby increasing the cup displacement. Among these three factors, the cup thickness had the greatest impact. Further, increasing the number of screws could enhance cup stability, and extra screws might be needed to ensure adequate stability of a thin cup.