The present work discusses the problem of dynamic stability of a viscoelastic circular cylindrical shell, according to revised Timoshenko theory, with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement. Proceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation. For a wide range of variation of physical mechanical and geometrical parameters, the dynamic behavior of the shell is studied. The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown. Results obtained using different theories are compared.