Bearing capacity calculations are an important part of the design of foundations. Most of the terms in the bearing capacity equation, as it is used today in practice, are empirical. Shape factors for square and rectangular footings could not be derived in the past because three-dimensional bearing capacity computations could not be performed with any degree of accuracy. Likewise, depth factors could not be determined because rigorous analyses of foundations embedded in the ground were not available. In this paper, the bearing capacities of strip, square, circular and rectangular foundations in clay are determined rigorously based on finite element limit analysis. The results of the analyses are used to propose rigorous, definitive values of the shape and depth factors for foundations in clays. These results are helpful in reducing the uncertainties related to the method of analysis in bearing capacity calculations, paving the way for more cost-effective foundation design.