Abstract: The multi-block upper bound method is used to calculate the bearing capacity of rough strip foundations on soils with anisotropic and non-homogeneous cohesion strength. Firstly, the anisotropic and non-homogeneous characteristics of the cohesion strength is taken into the calculation by the multi-block upper bound method. To examine the results of the multi-block upper bound method, comparisons are made with other existing results. It can be found that, the present results of the multi-block upper bound method are better, especially when the non-homogeneous coefficient and the internal friction angle are large. Secondly, the values of for large variation range of anisotropic and non-homogeneous coefficients are presented in figures, and the changing law of to anisotropic and non-homogeneous coefficients is discussed. Finally, the failure envelopes relating to different non-homogeneous coefficients are given by the multi-block upper bound method, and the changing law of the failure envelopes to the non-homogeneous coefficients is analyzed to expose the influences of the non-homogeneous coefficients on the values of