When carrying out research and technological processes in modern science and technology, the suppression or reduction of vibrations is often required for better operation of sensitive equipment and precision instruments. This paper presents a study on the damping of vibrations of a beam caused by the action of a dynamic load. The motion of an isotropic elastic beam is described using the model of S. P. Timoshenko. The beam has hinged supports at the edges. Damping moments located and acting at the anchoring points of the beam are used to damp the vibrations. As the beam moves in the hinges, a frictional moment with linear viscous damping occurs, which is proportional to the damping coefficient and the angular velocity of the beam in the hinge. In order to estimate the vibration damping, the solution of the direct problem of modeling the motion of the Timoshenko beam at zero ini- tial conditions is considered. The beam motion is modeled by a system of differential equations according to the model of S. P. Timoshenko. The re- quired functions are set in the form of Fourier series. Laplace integral transformation is used. The peculiarity of solution of a direct problem is that at this stage the friction moments in joints are unknown and are defined by solving corresponding inverse problem using Volterra integral equation the- ory. An analytical and numerical solution of the practical problem is obtained. Numerical results have been obtained in the form of graphs of beam point displacements and friction moments for different damping coefficients. A comparative evaluation of vibration reduction for different damping parameters has been carried out. The research results compare well with the results obtained by other authors.