In geotechnical investigation, determination of the bearing capacity of foundation soil constitutes is an important task. Most of the previous studies investigated the stability of such foundation system using classical bearing theory. The classical bearing theory was developed depending on the theory of plasticity with the assumption that the soil behaves as a rigid-plastic material. The bearing capacity theories require making a guess on the shape and geometry of the most critical failure surface (mechanism of failure) a priori. Most theories assumed the geometry of the failing soil mass is symmetrical with respect to the center of the footing, while, Krey suggested that the geometry of the failing mass is unsymmetrical. Numerical methods do not require an initial assumption the geometry of the failure mode. In the present work, a numerical study assisted by a computer program is carried out using (Krey's method) to investigate the center of the slip circle gives the minimum bearing capacity of the footing. Also, PLAXIS 2D used for analysis of some cases of studies by Krey's method. Krey it's of the present study is compared with the classical theories of the ultimate bearing capacity. The predicted values of ultimate bearing capacity of soil of this study are less than those of others theories of ultimate bearing capacity. In order to facilitate the calculation of bearing capacity the proposed equations are used. It is a function of (footing width, (B), ratio of footing depth to its width, (Rf) , angle of internal friction of soil,