A method is presented for the computation of the dynamic response of multi-story elastic-perfectly plastic frames. The development is based on a model in which the mass of the frame is assumed to be concentrated at the floor levels. The flexibility of the model is the same, member for member, as the actual structure. The equations of motion are written in terms of the deflections at the floor levels and are solved by means of a single-step forward-integration procedure. In these equations, the structural resistance to deformation may be expressed explicitly in terms of the floor deflections for any state of elastic-plastic behavior occurring during the dynamic response. In this formulation of the structural resistance, combined yielding of beams and columns is taken into account, and dynamic response curves are shown for several examples. The application of the method is extended to the analysis of statically loaded elastic-plastic frames. The latter application of the method is shown in several examples, and the results are compared with exact static analyses.