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Offshore wind turbines (OWTs) are affected by wind, wave, and current during their service life, which lead to the substructures undergoing combined effects of complex lateral loads and local scour. This phenomenon poses a significant challenge to the bearing capacity and cyclic responses of the widely used rigid monopiles for OWTs. This study develops three-dimensional numerical model to investigate the behavior of a rigid monopile subjected to lateral monotonic and cyclic loads, considering the stress history alteration induced by local scour. The hysteresis and plasticity accumulation of soils are captured by a bounding surface model. An accurate and concise semi-implicit stress integration scheme is creatively proposed to effectively incorporate this advanced constitutive model into the finite element (FE) software. The numerical model is verified by comparing FE results with centrifuge test results. Subsequently, the key factors such as cumulative deformation characteristics and bending moments distribution are investigated under different scour and cyclic loading conditions. The results indicate that with the facilitation of proposed semi-implicit scheme, the bounding surface model is capable of capturing the deformation pattern and cumulative deformation behavior of laterally loaded rigid monopile, and the cyclic responses of the monopile are significantly affected by the local scour. [ABSTRACT FROM AUTHOR]