A one degree of freedom elasto-plastic oscillator subject to stationary Gaussian white noise has a plastic displacement response process of intermittent character. During shorter or longer time intervals the oscillator vibrates within the elastic domain without undergoing any plastic displacements. These pieces of elastic response cannot be distinguished from conditional Gaussian response samples given that they are within the elasticity limits. Therefore, suitable Gaussian process theory can be applied to these pieces. Typically the plastic displacements occur in clumps of random plastic displacements alternating in the two opposite displacement directions. These plastic displacements can be evaluated with respect to distribution by use of Slepian model process considerations and simulation. This paper deals with the problem of determining, an accurate evaluation of the distribution of the waiting time between the clumps of plastic displacements. This is needed for a complete description of the plastic displacement process. A quite accurate fast simulation procedure is presented based on an amplitude model to determine the short waiting times in the transient regime of the elastic vibrations existing from a clump of plastic displacements has terminated and until approximate stationarity has been reached. Beyond this regime an additional waiting time is generated from an exponential distribution consistent with the upper tail of the waiting time distribution. (C) 2001 Elsevier Science Ltd. All rights reserved.