An approach to the analysis of deformation and stability of three-layer cylindrical panels and connected conical-cylindrical shells with honeycomb core is presented and justified. The central layer of these three-layer structures is fabricated using FDM-technology, while face layers are composed of carbon fiber reinforced polymer. These structures are used as structural elements across a diverse range of constructions. The study investigates the global stability and deformation of three-layer structures under the action of dual axial and radial loads. Furthermore, the impact of curvature radius on stability characteristics is examined. The finite element method, implemented in ANSYS, is employed to solve the problem. Two finite element models are developed for assessing global stability: an “exact” model the honeycomb core represented by its geometric, and an “approximate” model where the honeycomb core of the three-layer panel is replaced with an equivalent homogenized layer. The study reveals that the forms of global stability for cylindrical panels with varying curvature and plates are nearly identical. Additionally, critical loads obtained from both the “exact” and “approximate” models are nearly identical too. Investigation shows that when cylindrical panels deform under a longitudinal and radial loads, results obtained from calculations using both the “exact” and “approximate” models are similarly. Consequently, the use of a homogenized model for assessing global stability proves advantageous, reducing computation time. Leveraging this approach, the forms of global stability for connected shells under combined loads are determined.