Abstract. In this paper, the original methodology for taking into consideration internal friction forces is given in the example of nonstationary oscillations of a beam with elastically clamped edges. Bearing in mind the experimentally confirmed fact that the forces of internal friction practically do not affect the forms of structural vibrations, they are introduced into the equation of motion after separation of the spatial variable. This decomposition approach of forming a mathematical model in conjunction with the frequency independent Voigt hypothesis, with a known loss factor, made it possible to represent the solution in the form of spectral decomposition. For this purpose, we used the structural algorithm of the finite integral transform (FIT) method with the definition of the transformation kernel in the solution process. In fact, the proposed method is a method of quasinormal coordinates and represents an effective method of solving dynamic problems for mechanical systems in the presence of internal friction forces.