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In this work the influence of geometry, load and material properties on the nonlinear vibrations of a simply supported viscoelastic circular cylindrical shell subjected to lateral harmonic load is studied. Donnell’s non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion. Obtained results show that the viscoelastic dissipation parameter has significant influence on the instability loads and resonance curves.