A comprehensive study is performed on the stiffness of a monopile foundation supporting an offshore wind turbine in undrained, over-consolidated clay having a spatial variation of the soil properties. The undrained shear strength is considered as a stochastic field with increasing mean value over depth. A nonlinear stochastic p–y curve is integrated into a finite difference scheme for calculation of the monopile response. A simple model of a wind turbine is constructed with equivalent uncoupled springs providing the foundation response at the pile-cap level. This is used to identify the first natural frequency of the structure interacting with the soil. The reliability index and low probability events of natural frequency as an important criterion for fatigue are obtained by the asymptotic sampling method.