Timoshenko type equations are used, taking into account the transverse shift. The shell has the properties of constructive anisotropy. Forced oscillations in the frequency range, including the first significant low-frequency resonances, are considered. The internal scattering of vibrational energy is taken into account by the method of complex amplitudes. The influence of a number of parameters on the amplitude-frequency characteristics (frequency response) of input compliance is investigated. A semi-analytical method of constructing a solution is used. In the case of a cylindrical shell freely supported at the ends, Fourier series are used in two coordinates. The problem of forced oscillations is solved by decomposing the amplitudes of displacements according to their own forms of oscillations. At the same time, the separation of equations for determining coefficients by harmonic numbers is provided. The algorithm on this basis allows you to quickly build the amplitudefrequency characteristics necessary for analysis.