The ability to predict the ultimate bearing capacity of a foundation is one of the most important problems in foundation engineering. To solve this problem, geotechnical engineers routinely use a bearing capacity equation that contains a number of empirical factors to account for foundation shape, depth and inclination. In this paper finite element analysis is used to predict the undrained bearing capacity of strip, square, rectangular and circular footings embedded in clay. From these analyses, rigorous shape and depth factors have been derived and are compared with previous numerical and empirical solutions in the literature. The bearing capacity behaviour is discussed and the bearing capacity factors are given for various cases involving a range of embedment depths and footing shapes.