An earthquake resistant structure will suffer large plastic deformations under strong ground motions. This paper presents a practical method to evaluate the maximum plastic displacement of a structure, when the latter is modelled as an elastoplastic oscillator. The method exploits the results from a rigid-plastic model possessing the same ratio between yield strength and mass as the actual elastoplastic oscillator. The rigid-plastic model is shown to give a good estimate of the maximum plastic displacement of an elastoplastic oscillator when the natural period of the actual elastoplastic oscillator is comparatively short or comparatively high. For medium-period oscillators, however, the rigid-plastic approximation needs to be corrected. The present paper provides an empirical formula to calculate the required corrections, whatever the oscillator and the earthquake. This formula leads to a good –and almost always conservative– estimate of the seismic ductility demand and makes the rigid-plastic approach readily applicable to seismic design.