Two methodologies are outlined 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, whereas the second approach utilizes mechanics of materials. Both methods yield similar results. The loss factor is predicted both for specially orthotropic as well as for generally orthotropic laminas, subjected to axial stresses and/or transverse shear. The results for the loss factor of the laminas are in good agreement with available experimental data. As follows from the numerical analysis, the loss factor of laminas of the facings is significantly affected by the angle of lamination. The loss factor of a sandwich beam is relatively insensitive to the frequency of vibrations, although the effect of this frequency on the loss factors of constituent materials may alter this conclusion.