For offshore gravity platforms founded on clay, an important foundation failure mode arises from cumulative shear strain under cyclic loads. The major contribution to this cyclic strain accumulation comes from wave loads in sea states of high intensities. To analyze this and similar cumulative damage mechanisms, a probabilistic storm profile model is developed. Slepian random process models are used to estimate the temporal evolution of the significant wave height HS during a storm, during which HS exceeds a specified threshold. To predict storm profiles associated with any threshold, the model requires only conventional marginal wave statistics along with limited correlation information. Numerical results are shown for a North Sea location, where rare, high-threshold events can be verified by long hindcast histories. For an example foundation, predicted strain accumulation is compared with results from conventional storm profile models.