<p>By using the equations of three-dimensional linearized theory of stability of deformable bodies, we study the plane-deformation problem of compression of a homogeneous infinite strip along the internal open crack. An approach based on reducing boundary-value problems for potential harmonic functions to Fredholm integral equations of the first kind deduced in the general form for a broad class of highly elastic materials whose potential has the same roots of the characteristic equation is tested for the first time for regions bounded in one of the spatial directions. In the case where a symmetric form of the loss of stability is realized in the course of compression of a strip with harmonic-type potential, we determine the values of critical relative shortenings and analyze their dependence on the relative width of the strip.</p>