Abstract: Sandwich systems, consisting of two stiff face sheets and a compliant core, may exhibit complex instability behaviour due to the interaction and competition between local wrinkling and global buckling under compressive loading. To address this problem, this study develops a unified analytical model based on the energy analysis. Compared with traditional models that often adopt simplified displacement assumptions or neglect interfacial effects, the proposed model introduces a more complete in-plane displacement formulation that includes higher-order deformation modes and explicitly considers the interfacial shear between the core and the face sheets. This model enables simultaneous prediction of both local and global instability modes, while quantitatively revealing the competition and selection mechanisms between them. The model predictions show good agreement with finite element analysis (FEA), confirming the accuracy and robustness of the theoretical approach in capturing the critical buckling behaviour of sandwich structures. Under the ideal condition, the antisymmetric local-wrinkling mode has lower energy than the symmetric or single-sided modes, making it more likely to occur during instability. Furthermore, parametric analyses are conducted to investigate the effects of geometric parameters, such as the core-to-face thickness ratio, and material parameters, such as the modulus ratio, on the critical compressive strain and wavelength for local wrinkling. The results demonstrate that the proposed unified model provides higher accuracy than existing theoretical models. Based on the energy analysis, phase diagrams delineating the transition between local wrinkling and global buckling regimes are quantitatively constructed, which clearly identify the dominant instability modes under different parameter conditions and provide an explicit scaling relation for the critical local-to-global transition. These findings not only offer a rapid assessment tool for engineering design but also provide valuable insight into the underlying mechanics of flexible layered structures subjected to compressive loads, particularly in applications involving sandwich panels in aerospace, civil, and flexible electronics.