A generalized multi-mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story-specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three-dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight-story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright (c) 2014 John Wiley & Sons, Ltd.