Tripod suction bucket foundations are increasingly used to support offshore wind turbines (OWTs) due to their economic advantages and high overturning resistance. In the harsh marine environment, OWT tripod bucket foundations are subjected to long-term lateral cyclic loads from wind, waves and current. However, the response of tripod bucket foundations in clay to cyclic lateral loads is not well covered in the literature. Therefore, a three-dimensional (3D) numerical method is developed for analyzing their lateral cyclic response based on a simplified bounding surface model of clay. The numerical model is validated by comparing its results with scaled model test results available in the literature. The validated model is then used to investigate the rotation mechanism of tripod suction bucket under lateral monotonic and cyclic loading. The ‘bonded contact’ and ‘separable contact’ were set between the soil plug and the inner wall to simulate the upper limit and the lower limit cases of the tensile capacity of the suction bucket. The influences of the bucket-soil contact condition, loading direction and cyclic loading mode (one-way and two-way) on the cyclic behavior were analyzed. It was found that these factors have a significant impact on the cyclic responses, permanent rotation angle and failure mechanism of the tripod bucket foundation. The findings from this study can provide guidance for the design of OWT tripod bucket foundations.