The plane quasi-static problem on the non-linear deformation of a thin elastic layer stuck to an elastic half-space is studied. The half-space and the layer are uniformly compressed in the layer direction. It is assumed that before the deformation there is a crack between the half-space and the layer. The conditions of the crack opening and propagation are found. The problem is solved in one-dimensional formulation approach, in which the layer is modeled by Kirchhoff's plate and the contact forces are assumed to be the given functions of the layer displacement. The crack propagation begins when the displacement attains the prescribed critical value.