AbstractThe step‐by‐step modal time history integration methods are developed for dynamic analysis of non‐classically damped linear structures subjected to earthquake‐induced ground motions. Both the mode displacement and mode acceleration‐based algorithms are presented for the calculation of member and acceleration responses. The complex‐valued eigenvectors are used to effect the modal decoupling of the equations of motion. However, the recursive step‐by‐step algorithms are still in terms of real quantities. The numerical results for the acceleration response and floor response spectra, obtained with these approaches, are presented. The mode acceleration approach is observed to be decidedly better than the mode displacement approach in as much as it alleviates the so‐called missing mass effect, caused by the truncation of modes, very effectively. The utilization of the mode acceleration‐based algorithms is, thus, recommended in all dynamic analyses for earthquake‐i