This study investigates the buckling and post-buckling behaviour of functionally graded (FG) with auxetic core sandwich plates using a validated nonlinear computational framework. An in-house MATLAB formulation is developed based on First-Order Shear Deformation Theory and von Kármán geometric nonlinearity to model five distinct gradation laws power law, sigmoidal, tanh, exponential, and logarithmic along with corresponding auxetic core configurations. The material properties used in the analysis are obtained from prior experimental work on Al–SiC FGMs synthesized through powder metallurgy and characterised using nanoindentation. The proposed formulation is verified against established results for FG plates, honeycomb sandwich structures, and laminated composites, demonstrating good agreement. Comprehensive parametric studies assess the influence of aspect ratio, inhomogeneity exponent, gradation profile, core-to-facesheet thickness ratio, and boundary conditions on critical buckling loads and post-buckling response. The buckling analysis of sandwich composite plates with different models was calculated, as we increase the thickness of the core, the nondimensionalized buckling load decreases. Similarly, as the thickness of the plate decreases, the non-dimensionalized critical buckling load increases. With the above models, the power law, the sigmoidal law, and the tanhx law give approximately similar values of buckling load, whereas the exponential and logarithmic laws give similar results. Totally ceramic plates often provide the highest critical buckling loads. Regardless of the functionally graded plate's type or aspect ratio, the uniaxial buckling load can be twice that of the biaxial one. Parametric investigations showed that increasing the inhomogeneity exponent or core thickness decreases the nondimensional critical buckling load, while thinner plates enhance structural stability. Auxetic cores consistently reduce global stiffness and critical buckling loads relative to conventional cores. Post-buckling analyses further revealed that initial geometric imperfections expedite buckling initiation but enable greater load-carrying capacity at large deflections. Overall, the computational framework offers an effective predictive tool for assessing stability and designing advanced, lightweight FG and auxetic sandwich structures.