This study established a numerical model for soil-structure interaction (SSI) to examine the effects of the spatial incidence angle of SV waves and soil nonlinearity, utilizing viscoelastic artificial boundaries (VAB) and equivalent nodal force (ENF) method. Both the foundation's and superstructure's torsion and rocking responses were then analyzed. The findings indicate that subjected to spatially oblique incident SV waves, the rectangular foundation primarily has the rocking response while the torsional response is negligible. Furthermore, the maximum torsional and rocking angles about the x-axis at each frame floor are significantly enlarged by comparison with the perpendicular incident case. Moreover, the soil nonlinearity could increase the foundation's rocking angle and enlarge the maximum torsion and rocking responses of the structure's floors. Consequently, structural seismic damage assessment requires considering both the soil nonlinearity and incident seismic wave angles.