This research describes the impact of vertical earthquake components on the performance of typical non-ductile bridges. To achieve this goal, this research chooses a non-seismically designed reinforced concrete bridge typically found in the California area. Particularly, their columns with inadequate design have a higher possibility of shear failure. To consider this failure, the column model reflects shear-axial interaction effect and is verified by comparing simulated results and experimental data available in literature. Two computational bridge models having column shear model subjected to constant and varying axial load are then built to conduct inelastic dynamic analyses. The responses are employed to construct probabilistic seismic demand models for two bridge models. This results indicate that the consideration of shear-axial interaction effect increases the seismic demand of all bridge components in non-ductile bridges, resulting in their increased seismic vulnerability.