Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff--Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.