This article focuses on the dynamic behavior of a cylindrical shell (elastic or visco-elastic) contacting with ideal (or viscous) liquid. The problem of wave propagation in a cylindrical shell filled or submerged liquid has great practical importance. The phenomenon of wave-like motion of the fluid in the elastic cylindrical shells attracted the attention of many researchers [1, 2, 3, 4, 5, 6]. In these works devoted to wave processes in the elastic cylindrical shell - ideal liquid, used and refined classical equations of shells, consider the influence of the radial and longitudinal inertial forces, considered the average density of the flow of liquid or gas. In works [7, 8, 9] analyzes the laws of wave processes in an elastic shell with viscous fluid in the model of the linear equations of hydrodynamics of a viscous compressible fluid. Unlike other systems are cylindrical shell (elastic or viscoelastic) and liquid (ideal or viscous) is regarded as inhomogeneous dissipative mechanical system [10, 11, 12].