Abstract Thin-walled structural elements such as plates, panels, and shells of variable thickness are widely used at present in engineering, machine-building, and construction. Modern technologies allow creating any structural elements of a given shape, material, and the law of thickness variation. Therefore, the solution to the problems of the statics and dynamics of plates, panels, and shells of variable thickness, considering the real properties of the material, is relevant. Nonlinear parametric oscillations of viscoelastic orthotropic shallow shells of variable thickness are considered in the paper. Using the Kirchhoff-Love hypothesis, a mathematical model of the problem is constructed in a geometrically nonlinear statement. To describe the viscoelastic properties of a shallow shell, the hereditary Boltzmann-Volterra theory with the Koltunov-Rzhanitsyn relaxation kernel is used. To obtain resolving equations of the problem, the Bubnov-Galerkin method was used in combination with the numerical method. The effects of various physico-mechanical and geometrical parameters of a shallow shell of variable thickness were investigated.