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 problem by using the finite-element method in the finite element program ANSYS. The cylindrical shell consists of two layers with different elastic modulus. The inner layer (bandage) of the cylindrical shell is made from a rigid polymeric material with relatively high Young’s modulus. The outer layer is unknown and made from a softer polymer. Layers are considered homogeneous and isotropic. For the identification of the elastic modulus of the outer layer the TWCS method (Method for the Identification of the Elastic Properties of Polymer Materials by Using Thin-Walled Cylindrical Specimens) is considered. The contact problem is solved by using the Finite Element Method. The deformation of a thin polymer shell is characterised by great displacements and relatively low elastic deformations in a large range of movement of parallel planes. According to the above mentioned method at first the so-called reduced elastic modulus Epriv (modulus of inelastic buckling) is determined from the compression experiment of a cylindrical shell. The cylindrical shell is assumed to be single-layered with thickness t=t1+t2. Then the step-down ratio for the elastic modulus K=E1/Epriv is introduced. Further a Finite Element model for the problem of compression of a two-layer cylindrical shell is built by using software package ANSYS. The series of calculations of the cylindrical shell with different elastic modulus of the outer layer are carried out. Obtained results are tabulated and then on the basis of theses tables the graph of the dependence of the relative Young’s modulus E1/Epriv from the logarithm of the ratio of the elastic modulus of layers lg(E1/E2) is constructed.