The structure examined in this article is a sandwich structure comprising seven layers. Four of these layers are made of aluminum, designed to enhance strength and distribute the load across the structure. Two other layers are made of metallic foam, with three types of foam being analyzed in this study. The remaining layer, acting as the core, features a honeycomb cell structure with auxetic properties. Due to its lightweight and blast-resistant characteristics, this structure is extensively used in the aerospace industry. The aim of this research is to prolong the lifespan of the sandwich structure by achieving optimal strength. The structure is subjected to axial loading, leading to buckling. Therefore, this paper investigates the nonlinear buckling and post-buckling behavior of the structure. Initially, the mechanical properties of the foam and honeycomb are formulated, followed by the extraction of equations based on the Euler-Bernoulli beam theory. The Ritz method is employed to solve these equations. The innovation of this research lies in the fact that such a structure has never been subjected to buckling in previous studies. The findings reveal that increasing the honeycomb cell angle and reducing the porosity coefficient enhance the structure's strength.