Several studies of retrieved glenoid components from total shoulder arthroplasty show an erosion of the rim, surface irregularities, component fracture and wear resulting from polyethylene deformation in vivo. Particles resulting from polyethylene wear might be one of the reasons for the very high rate of glenoid component loosening found clinically. Because wear can be the result of high contact stresses, the aim of this study is to find out whether or not contact stresses are high enough to cause wear of the glenoid component and what influence the component type and geometry have on polyethylene contact stresses for different humerus abduction angles. Elasticity theory is used in a parametric study of contact stresses in several glenoid component designs. A finite element method is used to confirm the accuracy of the analytical solution. The analysis shows that the peak stress generated in glenoid components under conditions of normal living can be as high as 25 MPa; since this exceeds the polyethylene yield strength, wear and also cold flow of the components can be expected. It is predicted that more conforming components have lower contact stresses, which might result in lower wear rate and less cold flow. It is also found that a metal-backed component promotes higher contact stresses than an all-polyethylene component with the same total thickness, therefore it can be expected that metal-backed components have inferior wear properties.