In the framework of the general theory of stability (GTS) the method for the investigation of the stability loss problems of the elements of constructions fabricated from the non-aging linear viscoelastic composite materials is proposed, with an example problem. The proposed approach is based on the investigation of the development of the initial insignificant imperfection of the considered elements of constructions in the framework of the geometrical non-linear exact equations of the deformable solid body mechanics. All investigations are carried out on the clamped strip. The numerical results (critical time) obtained in the framework of the proposed approach are compared with the numerical results found in the framework of the displacement based third order refined plate theory. (C) 2001 Elsevier Science Ltd. All rights reserved.