The brittleness of ceramics has been their weak spot when considering them for total hip replacements. There are several situations from which concentrated stresses can develop and induce failure of the components. It is not a problem of the material’s properties in particular but also its design. This means that even proof tested-third generation-ISO obeying ceramics may fail if the incidence of the design parameters on them is not carefully evaluated. In this paper, the finite element analysis technique is used to show how the change of ball diameter can affect the Vonmises stress on the ball head component when it is subjected to a high (trauma-like) load. The analysis is nonlinear and was carefully tested for convergence. 3D models of four different ball head diameters where constructed, two designs of the bore/cone interface with two sets of material properties (Alumina and Zirconia) were considered. The results from these analyses are given in the form of stress maps on the ball heads; such data may be useful for surgeons, patients, and designers because it shows a direct relationship between two important parameters on ball head design (diameter and bore) and material properties, on the stresses that can cause failure of the component when they are concentrated in small elements of volume.