The standard methods for determining the elastic modulus of polymeric materials are based on tension test. The technique suggested in the present study can also be regarded as alternative. This methodology is based on the solution of a geometrically nonlinear problem of transverse deformation of thin walled circular cylindrical shell. The account of nonlinear effects makes it possible to use a considerably wider range of the loading curve in the elastic area of deformation, thus increasing the accuracy of results. A number of loading diagrams were obtained for thicknesses in the range 0.05-1 mm and elastic modulus within 100-5000 MPa. By choosing infinite values for the load and displacement, all the calculated curves were reduced to a unified universal loading curve. The methodology based on the planning of experiments and response surface technique has been developed for theconstruction of the universal loading diagram in dimensionless coordinates. This diagramm alow to solve the inverse problem of determination of the elastic modulus according to experimental points on the loading diagram. The optimisation problem for an circular shell has been formulated on the results of parametric study The finite element model of circular shell was built using ANSYS finite element program. The finite-element model constructed in the ANSYS program has the form of a quarter of a circular ring owing to symmetry. The boundary conditions correspond to the symmetry conditions. Since we consider thin-walled shells which can be subjected to great displacements and rotations, for different forms of elastic potentials, as a finite element we took a SHELL181 shell element, which corresponds to the requirements adopted. In the contact zone, a CONTA174 contact element is used. The simplicity of the experiment and the use of a wide range of the loading curve in the elastic region of deformation make it possible to obtain more initial data, which provides the higher accuracy in determining the flexural modulus.