The paper treats Finite Element Analysis (FEA) specific to the mechanical behavior of a structural layer cap type with polymer cellular cores within a pressure vessel. The layered composite structure comprises two outer polymer shells (synthetic glass/ plexiglass) and cellular polymer core with triangular shaped cells. This analysis uses the Autodesk Inventor 2016 Professional 3D design and modeling software, in conjunction with the FEA analysis program, ANSYS 14.5 - Workbench, using the Mesh module. Mechanical behavior of the structural models specific to the four types of test caps, each having different cellular polymer core (ABS, PLA, PC and CF, 3 and 5 mm thickness), is revealed through the analysis of the state of stresses and deformations and correlating the FEA simulation results with experimental testing. Since the analysis leads to quasi-equivalent results under identical conditions of application until the fracture of the caps, it is found that such an FEA approach of the mechanical system components occupies an important place in the modern design process, being one of the ways of identifying the deformation fields and equivalent stresses in the analyzed composite structures.