AbstractThe dynamic non‐linear behaviour of three‐dimensional long‐span cable‐stayed bridges under seismic loadings is studied. The cases of multiple‐support as well as uniform seismic excitations of these long and flexible structures are considered. Different sources of non‐linearity for such bridges are included in the analysis, as outlined in the companion paper. In this accompanying analysis a tangent stiffness iterative procedure is utilized to estimate the non‐linear seismic response. Numerical examples are presented in which a comparison between a linear earthquake‐response analysis (based on the utilization of the tangent stiffness matrix of the bridge at the dead‐load deformed state which is obtained from the geometry of the bridge under gravity load conditions) and a non‐linear earthquake response analysis using the step‐by‐integration procedure is made. In these examples two three‐dimensional bridge models representing recent and future trends in cable‐stayed bridge design are utilized. The study sheds some light on the salient features of the seismic analysis and design of these long contemporary bridges. In addition, parameters affecting the seismic response of these bridges are discussed: other factors considered are non‐linearity, uniformity and spatial variation of ground motion inputs