A mathematical model, methods and algorithm to assess the spatial natural vibrations of axisymmetric structures are given in the paper taking into account the variability of the slope and structure thickness in the framework of the viscoelastic theory of shells. Dissipative properties of the material are taken into account by the Boltzmann-Volterra hereditary theory of viscoelasticity. The spatial natural vibrations of high-rise ventilation pipes of the Armenian nuclear power plant (NPP) and smokestacks of the Novo-Angren, Syrdarya, Azerbaijan and Ekibastuz thermal power plants (TPP) were studied taking into account the elastic and viscoelastic properties of their material. The reliability of results was verified by comparing the results obtained with the exact solution of a number of test problems, as well as by comparing the results with the results of field experiments. It was found that when the viscoelastic properties of structure material are taken into account, the decrement of their vibrations weakly depends on the values of eigenfrequency. Along with this, the dangerous range of earthquake frequencies includes not only the bending frequencies of the structure, but the spatial ones as well.