The delamination of unidirectional composite materials takes place tinder compression along the reinforcing elements and often occurs near the free surfaces or planes of these materials. The first investigation in this field was made in 1976 and since then numerous studies have been carried out. However, the approaches developed in these investigations are applicable only to time-dependent composite materials. In the present paper, an approach for investigating unidirectional viscoelastic composite materials is proposed, with a particular problem as an example. The investigations are performed within the framework of exact three-dimensional geometrically nonlinear equations of viscoelasticity theory.