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The response of bucket foundations for offshore wind turbines subjected to cyclic loading in saturated clay is explored through three-dimensional finite element numerical analyses. In the analyses, nonlinear cyclic hysteretic behavior of clay under undrained condition is modeled through a simple kinematic hardening constitutive model embedded in ABAQUS. The finite element model is validated against published in situ tests of bucket foundations under quasistatic cyclic loading in Bothkennar clay. The computed results agreed generally with those from in situ tests. The behavior of bucket foundations with different aspect ratios under displacement-controlled cyclic loading mode is investigated. Then, the evolution of foundation displacement with increasing number of cycles is studied subjected to wind and wave combined loading. The results show that, for the cycles of low-amplitude rotation, dimensionless moment-rotation curve is approximately elastic; however, the curve engenders obvious hysteresis loop, whose shape is influenced by soil-sidewall interface condition, during high-amplitude cycles. Under thousands of loading cycles, for bucket foundations of low aspect ratio, the oscillatory displacement component is smaller; however, the residual component will accumulate gradually until the serviceability rotation is exceeded. For foundations of high aspect ratio, the oscillatory component is relatively larger, but the accumulation rate of residual displacement decreases gradually.