Debris resulting from damage to the surface of polyethylene components of total joint replacements has previously been shown to contribute to long-term problems such as loosening and infection. Surface damage has been associated with fatigue processes due to stresses arising from contact between the metal and polyethylene components in these prostheses. In the present study, we used elasticity and finite-element solutions to determine these stresses for total hip replacements with head diameters of twenty-two and twenty-eight millimeters and for a condylar total knee replacement. We also examined the effect on these stresses of using carbon-fiber-reinforced polyethylene instead of plain polyethylene. Stresses associated with surface damage in the tibial component of the total knee replacement were much larger than those in the hip replacements. The analysis of contact stress as a function of thickness of the polyethylene insert for tibial components showed that a thickness of more than eight to ten millimeters should be maintained when possible. The contact stress in the tibial components was reduced most when the articulating surfaces were more conforming in the medial-lateral direction. Contact stresses were much less sensitive to changes in geometry in the anterior-posterior direction. For the hip components, the stresses were lower in the acetabular component of the twenty-eight-millimeter hip replacement than in the twenty-two-millimeter replacement. The use of carbon-fiber-reinforced polyethylene resulted in stresses that were higher by as much as 40 per cent. Because the contact area between articulating surfaces moves during flexion, portions of the surface will be subjected to cyclic stresses. The contact area for the knee replacements in flexion was smaller than for the hip replacements, and the range of the maximum principal stress was larger. Consequently, the combination of the higher stress and the moving contact area is more likely to cause surface damage due to fatigue in tibial components than in acetabular components, which is consistent with clinical observations.