Two similar continuum plasticity material models are used to examine the influence of material modelling on the seismic response of reinforced concrete frame structures. In the first model reinforced concrete is modelled as a homogenised material using an isotropic Drucker–Prager yield criterion. In the second model, also based on the Drucker–Prager criterion, concrete and reinforcement are included separately. While the latter considers strain softening in tension the former does not. The seismic input is provided using the Eurocode 8 elastic spectrum and five compatible acceleration histories. The results show that the design response from response history analyses (RHAs) is significantly different for the two models. The influence of compression hardening and strength enhancement with strain rate is also examined for the two models. It is found that the effect of these parameters is relatively small. In recent years there has been considerable research in nonlinear static analysis (NSA) or pushover procedures for seismic design. The NSA response is frequently compared with that obtained using RHA, which also uses the same material models, to verify the accuracy of the static procedure. A number of features exhibited by reinforced concrete during dynamic or cyclic loading cannot be easily included in a static procedure. The design NSA and RHA responses for the two material models are compared. The NSA procedures considered are the Displacement Coefficient Method and the Capacity Spectrum Method. A comparison of RHA and NSA procedures shows that there can be a significant difference in local design response even though the target deformation values at the control node are close. Moreover, the difference between the mean peak RHA response and the pushover response is not independent of the material model.