The paper outlines two methodologies for the analytical evaluation of the loss factor in composite laminates and in sandwich structures. One of these methods is based on the analysis of free vibrations, while the second approach utilizes mechanics of materials. The loss factor can be predicted both for specially orthotropic as well as for generally orthotropic laminae, subjected to axial stresses and/or transverse shear. The results for the loss factor of the laminae are in good agreement with available experimental data. As follows from numerical examples, the loss factor of polymer-matrix composites increases with the lamination angle and experiences relatively small variations at large values of these angles.