In this paper we seek closed-form solutions for the problem of failure of a strip foundation on undrained clay subjected to combined vertical, moment and horizontal loading. The motivation for the study comes from the offshore oil and gas industry, where the understanding of problems of foundations under general loading is important. The contact between the foundation and the clay is unable to sustain tension, and this feature of the problem considerably complicates the solution. It is found that the bound theorems of plasticity theory are insufficient to solve the problem, and a solution can only be found by adopting certain further hypotheses. Although the existence of an exact solution cannot be proven, apparent upper and lower bounds to a plausible solution are obtained. In order to derive these solutions, a new scaling procedure is introduced, which plays the same role for upper bounds as does the effective width method for lower-bound footing collapse loads.