Obliquely incident seismic waves have been habitually overlooked in fragility analysis. In this paper, a new approach to solving the equivalent loads on the infinite element boundary due to obliquely incident seismic waves is proposed. Based on the site conditions and structural characteristics in the Jiaxing area, the seismic response of a multi-story reinforced concrete (RC) frame structure has been fully investigated through the finite element method. Under obliquely incident SV waves (shear wave in the vertical x-z plane), the distribution of internal forces on the structure in the case of homogeneous foundation soil is significantly asymmetrical. Among the 3 obliquely incident angles investigated in this paper, the maximum inter-story displacement is smallest when the incident angle is 20° and largest when the angle equals 30°. For the structural fragility, the exceedance probability at each structural damage level is smallest when the incident reflection angle is 20° and largest when the angle equals 30°. When the structure is located in the silty valley, the influence of oblique incidence is attenuated and there is no obvious stress asymmetry on the structure due to the refraction of seismic waves on the interface.