The paper presents a numerical method and algorithm for solving tasks in dynamics of viscoelastic thin-walled elements in structures of variable thickness. The equations of motion concerning deflections are described by partial integro-differential equations (PIDE). Using Bubnov-Galerkin’s method, based on the polynomial approximation of deflections, the task is limited to the study of the system of ordinary IDEs, where the independent variable is time. The solution to the system of IDEs is obtained by the offered numerical method, which results into the algorithm of the numerical solution and the program in the Delphi algorithmic language. The study of nonlinear vibrations of thin-walled elements in structures, allowing for variable thickness in the geometrical nonlinear statement, has enabled revealing a number of mechanical effects. Depending on physico-mechanical and geometrical parameters of the considered viscoelastic thinwalled elements in structures, the authors reccommend how to use the rigidity of the system.