Reinforced viscoelastic cylindrical shells with deformable fillers are used in rocketry, aircraft construction, shipbuilding, and construction. To give greater rigidity, the thin-walled part of the shell is reinforced with ribs, while a slight increase in the weight of the structure significantly increases its strength, even if the ribs are of low height. The purpose of this work is to develop a technique, algorithm and programs for finding resonant frequencies and modes of vibration for circular ribbed viscoelastic cylindrical shells under various boundary conditions. The paper deals with vibrations of longitudinally reinforced cylindrical shell structures with a filler. The variation principle is used to study the vibrations of a thin longitudinally reinforced viscoelastic cylindrical shell under dynamic influences. Oscillatory processes of the filler and the bonded shell satisfy the Lame equations. At the contact between the shell and the filler, the conditions of rigid contact are fulfilled. The relationship between stresses and strains, for a linear viscoelastic material, is represented in the form of the Boltzmann-Voltaire integral.