The paper deals with dynamic hysteretic oscillators without post-yielding hardening, called ideal elasto-plastic oscillators, subjected to white noise. They are characterized by the fact that they do not reach stationarity even though excited by stationary stochastic processes. A simpliยฎed solution procedure to capture this behaviour is presented in this paper. It is based on modelling the accumulated plastic deformations as a homogeneous compound Poisson process. In particular, two aspects are addressed in the paper: (1) evaluation of the probabilistic parameters of the accumulated plastic deformation process; and (2) evaluation of the second-order cumulants of the response by means of closed form expressions. Although the presented results are not rigorous and rely on an empirical basis, the aim is a very handy and sufยฎciently accurate procedure to obtain the evaluation of the second-order probabilistic parameters of elasto-plastic oscillators. Moreover, by testing this procedure against Monte Carlo simulations, a parametric study has been conducted in order to assess the range of validity of the homogeneous compound Poisson process model. The presented procedure can be easily extended to the case of non-normal delta correlated input processes.