The object of research is steel vertical cylindrical tanks for the storage of petroleum products with imperfect geometric shapes. The purpose of this work is to develop and test a new method of numerical solution of differential equations on the example of computer modeling of the stress-strain state of the tank from the hydrostatic load; taking into account geometric and structural nonlinearity. The method of numerical solution of the differential equations is based on the geometrical theory of multidimensional interpolation implemented in the point calculus. Computer methods of calculation and visualization of modeling results were performed with the help of the computer algebra system Maple. To compare the modeling results; a reference solution was obtained in the software package of finite element analysis SCAD. The calculations were carried out following the strength theory of octahedral tangential stresses or specific energy of deformation (Huber-Hencki-Mieser energy theory). Results. The differential stress modeling equation for an elastic cylindrical shell under axisymmetric loading has been improved for the numerical analysis of the stress-strain state of a cylindrical tank with geometric imperfections. A new method of numerical solution of differential equations using geometrical interpolants has shown a high level of accuracy and higher speed as compared to the existing methods. A numerical solution of the stress-strain state of the tank wall with geometric imperfections in the form of a 6th-degree polynomial was obtained. A new engineering methodology for the examination of the technical condition of operating tanks for the storage of petroleum products with geometric imperfections has been proposed.