Suction caisson foundations are increasingly used as foundations for offshore wind turbines. This paper presents a new, computationally efficient, model to determine the stiffness of caisson foundations embedded in linearly elastic soil, when subjected to six degree-of-freedom loading; vertical (V), horizontal (Hx, Hy), overturning moment (Mx, My) and torsion (T). This approach is particularly useful for fatigue limit analyses, where the constitutive behaviour of the soil can be modelled as linearly elastic. The paper describes the framework on which the new model is based and the 3D finite element modelling required for calibration. Analyses conducted using the proposed approach compare well with results obtained using 3D finite element analysis. The possibility of low-cost analysis, coupled with a simple calibration process, makes the proposed design method an attractive candidate for intensive applications such as foundation design optimisation.