Abstract: In this paper, the shakedown problem is dealt with of elastoplastic structures subjected to the quasi-statically varying loads within a given domain. The work-hardening yield surface of the material is assumed to be piecewise linear. A general inequality is presented, according to which, the generalized Melan's shakedown criterion as well as bounds on displacement and plastic strain are derived. Moreover, applications of the derived result are illustrated by a simple example.