It is well recognized that structures designed to resist strong ground motions should be able to withstand substantial inelastic deformations. A simple procedure has been developed in this paper to monitor the dynamic earthquake response (time-history analysis) of both steel and concrete multistorey buildings in the inelastic range. The building is treated as a shear beam model with three degrees of freedom per floor. The entire analysis has been programmed to run on a microcomputer and can output time histories of displacements, velocities, accelerations and member internal forces at any desired location. A record of plastic hinge formation and restoration to elastic state is also provided. Such information can be used in aseismic analysis and design of multistorey buildings so as to control the damage and optimize their performance.