Suction caisson foundations provide options for new foundation systems for offshore structures, particularly for wind turbine applications. During the foundation design process, it is necessary to make reliable predictions of the stiffness of the foundation, since this has an important influence on the dynamic performance of the overall support structure. The dynamic characteristics of the structure, in turn, influence its fatigue life. This paper describes a thermodynamically consistent Winkler model, called OxCaisson, that delivers computationally efficient estimates of foundation stiffness for caissons installed in homogeneous and non-homogeneous linear elastic soil, for general six degrees-of-freedom loading. OxCaisson is capable of delivering stiffness predictions that are comparable to those computed with three-dimensional finite-element analysis, but at a much lower computational cost. Therefore, the proposed model is suited to design applications where both speed and accuracy are essential, such as large-scale fatigue assessments of offshore wind farm structures. The paper demonstrates that the OxCaisson model can also be applied to short, rigid monopile foundations.