The purpose of the present investigation is to elaborate a method for determining the flexural modulus of a polymer material based on the solution of compression and tension problems by using the finite-element method in the finite element program ANSYS. To solve the nonlinear problem by the finite-element method, a macros-program was elaborated, which specifies the geometry, physical law, and properties of the material, boundary conditions, loading, division into finite elements, and the step scheme of the solution. The deformation of a thin polymer shell is characterized by great displacements and relatively low elastic deformations in a large range of movement of parallel planes. The solution obtained by finite element method allows making the universal loading diagram in dimensionless coordinates in the given range of thicknesses and elastic module. Equation of the universal loading diagram allows us to solve the inverse problem of determination of the elastic modulus according to experimental points on the loading diagram. The method of determination of the flexural modulus of thin polymer shells discussed above was successfully approved on a series of various kinds of thin PVC specimens by tension test. Than specimens was tested for vibration (modal) test in order to measure the eigenfrequencies and the corresponding modes. The flexural modules received by compressing a circular cylindrical were verified by comparing the experimentally measured eigenfrequencies with numerical results from ANSYS program. The method enables the use of a “single specimen principle”. For example, changes in the modulus caused by different processes affecting the structure and properties of polymer material, for example, different kinds of aging of polymer materials, absorption of liquids (water) and vapors by a certain material, and so on, can be studied on a solitary [on one and the same] specimen.