The method of determination of the elastic modulus is based on a solution to the problem of compression of a thin-walled circular cylindrical tube by two parallel planes. The contact problem is solved by the finite-element method (ANSYS). 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. This method was employed to calculate the elastic modulus for a series of experimental specimens consisting of five polymer compositions, whose elastic modulus have been found earlier via standard tension tests. The good correspondence between the results confirms the efficiency of the given method.