A randomly excited single‐degree‐of‐freedom oscillator in which an idealized form of plastic deformation can take place is studied. Through the use of an artificial process, statistics of this nonlinear, hysteretic system are deduced from linear system‐response statistics in two régimes of operation. The expected accumulated plastic deformation is found as a function of time and some other statistics derivable from the artificial process are indicated. A numerical example is given that illustrates the use of the method with low‐cycle fatigue data.