In this paper the cylindrical shell consisting of two layers with different elastic modulus is considered. The inner layer (bandage) of the cylindrical shell is made from a rigid polymeric material with relatively high Young’s modulus (103 MPa). The outer layer is made from a softer polymer - Young’s modulus 102 MPa or even 10 MPa. Poisson’s ratios of both layers are 0.35. 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 method is based on the solution of the problem of compression of a thin-walled cylindrical tube by two parallel planes. 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 Finite Element model is built by using SHELL181 element which allows multi-layer properties. Layers are considered homogeneous and isotropic. The series of calculations of the cylindrical shell of the radius R=50 mm, the thickness t=1 mm and the layer ratio t1/t2=1 are carried out. The length of the shell L=1. The Young’s modulus of the inner layer E1 =1000 MPa, for the outer layer three different elastic modulus is selected - E2=10, 100 and 1000 MPa. Further 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=25…200 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=25…200, which is the solution of the problem.