The object of study is a stationary Gaussian white noise excited multi-degree-of-freedom (MDOF) linear elastic, ideal plastic, linearly damped, statically determinate oscillator with several potential elements of ideal plastic yielding. Specifically the study is exemplified for a plane multistory shear frame with rigid traverses where all the connecting columns except the columns in one or more of the bottom floors have finite symmetrical yield limits. The white noise excitation acts on the mass of the first floor making the movement of the elastic bottom floors simulate a ground motion that interacts with the structure above the bottom floors. The method of study is so-called Slepian model simulation and is in principle the same for other statically determinate MDOF elasto-plastic oscillators of the considered type. The method is fast as compared to direct simulation and provides results that give good insight in the behavior of the plastic displacement response process. (C) 2003 Elsevier Ltd. All rights reserved.