Anisotropy and strength nonhomogeneity are common phenomena for clay foundation. However,the existing theories of bearing capacity calculation are mainly applicable to isotropic and homogeneous soils. Upper bound method is used to calculate the bearing capacity of rough strip foundations on clay with anisotropy and nonhomogeneity. The failure mechanism employed in the upper bound method has already been verified by other scholars to be the best one in multi-block upper bound method to calculate the bearing capacity of rough strip foundations on isotropic and homogeneous soils. To examine the proposed method,various calculations have been carried out. The results are compared with those of the characteristic method and other upper bound methods. It can be found that the proposed method gives the best calculation results among the existing upper bound methods in the literaturs. The effects of the anisotropy and strength nonhomogeneity on the values of the bearing capacity are then discussed. Failure envelopes can be obtained in the upper bound limit analysis and the mechanism for the influence of soil anisotropy and nonhomogeneity on the bearing capacity of foundation can be revealed. From the calculation results,it can also be found that the anisotropy and nonhomogeneity of soil affect not only the bearing capacity of foundation but also the location and shape of the failure envelopes.