The ultimate bearing capacity of shallow foundations placed near slopes has long been a critical issue, especially for the obliquely loaded case. However, it is too complicated to find a statically and kinematically admissible field and then present a rigorous solution. Herein, the method of rigorous characteristics is applied to establish a slip line field that satisfies the stress and velocity boundary conditions simultaneously. Meanwhile, five one-sided failure modes combined with basic boundary value problems are presented to consider a variation in the failure mechanism. The application of boundary value problems avoids an arbitrary assumption of the failure shape and identifies the failure region automatically. The analytical solutions are located in the narrow range determined by the upper bound and lower bound solutions found in the literature, and hence they are rigorous. The ultimate bearing capacity is estimated by accounting for the load inclination, soil properties and the geometry model. The variation in the ultimate bearing capacity and the failure mechanism of obliquely loaded cases shows great non-linearity, due to the complicated boundary conditions.

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