Up to now, numerous problems of the stability loss for elements of structures made from composite materials have been investigated in the framework of the three-dimensional linearized theory of stability (TDLTS). It follows from the analysis of these investigations that the TDLTS was mainly applied to the design of elements of structures made from time-independent materials. For the solution of these problems for viscoelastic materials in the framework of the TDLTS, the dynamic investigation method and the critical deformation method are recommended in many references. However, it is known that a very reliable and frequently used approach for viscoelastic materials is the approach based on the study of the growth of insignificant initial imperfections in elements of structures with time. Taking into account the above-mentioned, an approach based on the growth of the initial imperfection for the investigation of the stability loss problems of elements of structures made from viscoelastic composite materials in the framework of TDLTS is proposed in the present paper. The composite material is modeled as an anisotropic, viscoelastic solid with averaged mechanical properties and all investigations are made on the strip simply supported at the ends.