In this study, a hysteresis envelope mathematical model for the double extended end-plate bolted beam-to-column joint is proposed. The aim of a proposed joint model is to provide a more realistic behaviour of steel frames under seismic loading by using nonlinear static pushover analysis. The hysteresis envelope model defines the ratios between the monotonic properties of the joints and the properties of the joints during cyclic deformation. The proposed models are based on the hysteresis curves of the joints obtained by numerical simulations. The numerical model takes into account the geometric nonlinearity of the connecting elements, preloading of bolts, contacts between plates and bolts, and nonlinear properties of steel. Nonlinear static pushover analyses of steel frames are performed where the behaviour of the joints is described using the proposed hysteresis envelope models. The results are compared with the nonlinear static pushover analyses of steel frames with a trilinear monotonic joint model. Based on the results, the values of maximum peak ground acceleration for moment-resisting frames with the monotonic model of joints and hysteresis envelope model are estimated.