The Random Finite Element Method has been employed for calculating the random characteristics of bearing capacity of a strip foundation. The study has been carried out for two different soils; a greyblue clay from Taranto in Italy, which is well defined from a stochastic point of view, and a cohesionless soil with assumed stochastic characteristics. The authors have focused on developing a formulation, which includes anisotropic random fields of cohesion as well as the angle of internal friction. The effect of self weight has been incorporated for the first time in studying the bearing capacity of spatially variable soil. Results clearly show that the introduction of anisotropy into random fields is more realistic, and makes RFEM predictions more effective for design purposes.