Failure envelopes written directly in terms of the applied vertical, horizontal and moment loads are finding increased popularity in the design of shallow foundations. However, these are deterministically derived and assume a spatially homogeneous soil without any variation in properties. The spatially variability of soil strength under a strip footing is accounted for in the results of this paper through the Random Finite Element Method, which combines spatial variability analysis, finite element simulation and Monte Carlo simulation. A multitude of combined loading failure envelopes are derived from finite element analysis of a soil domain with randomly generated and spatially varying values. This has allowed the size and shape of the failure envelopes to be defined for distinct levels of their probability of occurrence. These provide guidance for the reliable design of strip footings on clays in heterogeneous soil conditions, and have particular application offshore where horizontal and moment loads can be proportionally large. © 2012 Elsevier Ltd.