The purpose of the present investigation is to solution of compression problem of thin cylindrical polymer shell with two layers by two planes in the finite element program ANSYS. The cylindrical shell consisting 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 made from a softer. The average radius R, the length L, the Young’s modulus of the inner layer E1 and the thickness of both layers t1 and t2 of the cylindrical shell are assumed to be known. The parameter to be identified is the elastic modulus of the outer layer E2. For the identification of the elastic modulus of the outer layer E2 the TWCS method (Method for the Identification of the Elastic Properties of Polymer Materials by Using Thin-Walled Cylindrical Specimens) is considered. The finite element model is built by using SHELL181 element which allows multi-layer properties and has the form of a quarter of a circular ring owing to symmetry. The boundary conditions correspond to the symmetry conditions. The deformation of a thin polymer shells 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 total thickness t. Then the step-down ratio for the elastic modulus E1/Epriv is introduced. 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. Also it was necessary to find out the influence of the geometrical parameter R/t on the elastic modulus of layers. On this reason the cylindrical shells of relative radius R/t were considered. Influence of this parameter appeared to be extremely small - within 0.3 %. Thus, the obtained graph of the dependence of the elastic modulus of layers from the ratio of the thicknesses of layers is true in the considered range R/t, which is the solution of the problem.