A strict upper bound solution to limit loads on strip footings over two-layer clay foundation soil is presented. Two mechanisms of failure are considered: one with a continually deforming field, and a rigid-block mechanism. The multi-block mechanism was found to be very flexible in terms of being able to assume different shapes of the deformation pattern. Consequently, this mechanism yielded the least upper bound to the bearing pressure. The method used was adapted to calculations of bearing capacity of strip footings subjected to loads with horizontal components. If the depth of the second layer of clay is sufficiently large, the shear strength of this layer will not affect the bearing capacity. This depth is referred to here as the critical depth, and it depends on the footing width and the combination of the undrained shear strength in the two layers. If the undrained shear strength of the bottom layer is small compared to the top layer, the critical height may be as much as twice the footing width.