Rectangular mudmat foundations are frequently used for supporting subsea structures for offshore oil and gas developments. The self-weight of the subsea structure and mudmat often mobilise a relatively small proportion of the vertical bearing capacity and horizontal–torsional sliding generally represents the governing load case. However, the effect of torsion on mudmat capacity is not explicitly considered in current guidelines for geotechnical design of offshore foundations. In this paper, upper-bound plastic limit analysis is used to develop explicit expressions for the combined horizontal and torsional capacity of skirted mudmats. The results of the limit analyses are compared with results from finite-element analysis, and with other published solutions. A method is proposed for estimating the translational sliding resistance from the interaction diagram for biaxial horizontal loading and a unique expression is proposed to define the normalised H–T failure envelope. The effects of foundation aspect ratio, foundation embedment ratio, skirt–soil interface roughness, direction of horizontal loading and degree of soil strength heterogeneity are investigated systematically.