Abstract <p>The application-oriented problem of two-stage compression of a plane layer (laminate), which is nonhomogeneous over the thickness and infinite in two directions, is considered. The constitutive relations of the layer material are consistent with the theory of small elastoplastic deformations. At the first step, one-dimensional compression takes place according to an active process described by a two-link polygonal line. At the second step, controlled unloading is carried out, as a result of which the thickness of the layer takes a given value at a given compression stress.</p>