Considering the unique characteristics of sandwich structures in the optimal design of lightweight and high-strength components, their application in advanced engineering systems has been steadily increasing. These structures exhibit superior performance, particularly under buckling loads, unwanted vibrations, and energy absorption conditions. In this study, two cylindrical sandwich specimens were fabricated, consisting of a thermoplastic polyurethane (TPU) hyperelastic core and composite face sheets. The main objective of the experiments was to evaluate the accuracy of predicting the critical buckling load using the Vibration Correlation Technique (VCT). One specimen was subjected to a destructive test, while the other underwent a non-destructive test. The VCT, as a non-destructive and cost-effective approach, estimates the critical load by monitoring the variations in the natural frequencies of the specimen under axial compression up to the onset of instability. Modal analyses were performed using the impact test method, and the effects of parameters such as core thickness and fiber orientation of the composite faces were investigated. In addition, a three-dimensional numerical model was developed in ABAQUS to analyze the structural behavior under different loading conditions. A comparison between experimental and numerical results showed a minor discrepancy (approximately 3.6%) in the predicted buckling load. The findings indicate that the VCT is a reliable and accurate tool for estimating the buckling load in modern sandwich structures with hyperelastic cores