The paper addresses analysis techniques and design parameters for suction caissons in clay for loading conditions ranging from horizontal to vertical. A three-dimensional upper bound approach is described for caissons undergoing significant horizontal motion or rotation, and the relative accuracy of the analysis is assessed through comparison with independent semi-analytical 3-dimensional finite element analyses. For vertical loading, design parameters for shaft friction and end-bearing are deduced from results of physical model tests, for both sealed and unsealed caissons and for short-term and long-term loading. Interaction between horizontal and vertical loading is discussed, and aspects such as strength anisotropy of the soil, mis-alignment of the caisson (vertically and in plane), and orientation of the applied load are considered.