It has been shown in recent years that the ground state of polymer-clay nanocomposites corresponds to phase-separated, intercalated, or exfoliated state dependent on external conditions. That is why the mechanism of structural transitions between such states is a subject of great scientific and practical importance. A simple "kink" model of melt intercalation in conditions of a shear flow proposed earlier [V. V. Ginzburg, O. V. Gendelman, and L. I. Manevitch, Phys. Rev. Lett. 86, 5073 (2001)] deals with the degenerate case when the energies of phase-separated and intercalated states are equal. Here, we consider a general, nondegenerate case, taking into account the nonequivalence of the aforementioned energies, and develop the model for the case of more general external stress conditions. The potential energy per unit area taking into account the enthalpic and entropic terms in the free energy of the confined polymer, as well as van der Waals and electrostatic interaction between the clays platelets themselves, is approximated by two parabolas. The analytic solution of the appropriate nonlinear dynamical problem has been found in strongly damped limit. Such a solution is manifested as loss of mechanical stability of the aggregated state. It is followed by formation of solitonic excitation, whose propagation leads to structural transition. As a result, we are able to compute the threshold compression force depending on external stress or shear flow intensity that provides the possibility of intercalation and to outline some kinetic peculiarities of the process. (C) 2003 American Institute of Physics.