This paper proposes a simplified procedure for the seismic vulnerability analysis of multi-span simply supported bridges, in the case of single piers with solid circular sections. The proposed method can be applied whenever the seismic response of the whole bridge depends on the most critical pier. For an assigned limit state, the procedure determines the capacity curve of the critical pier as a function of three parameters (elastic stiffness, displacement at yielding, displacement at collapse), starting from the behaviour under combined axial stress and bending, and then taking into account the different possible collapse modes (shear failure; lap splice failure of the longitudinal bars; buckling) and the geometric nonlinearity. A significant numerical example is presented in which the traditional FEM solution is compared with the proposed simplified procedure.