In this study, numerical models were developed with three different core widths and heights, and numerical analyses were performed to investigate the coupled effects of design parameters on stress and structural weight under gravitational prestress. In addition, the design parameters were optimized using the Response Surface Methodology (RSM), and thus core width and height were determined, providing minimum weight and maximum strength. The numerical findings were validated by comparing them to the statistical-based optimization results. On the other hand, thermal pre-stressed structural analyses were performed to assess the effect of the elasticity modulus and thermal expansion coefficients of the adhesives on the structural responses. The current study demonstrated that core width was more effective than core height on stress and deformation responses, and also that ascending core width had an adverse impact on bending stiffness. Furthermore, the optimum core width and height were determined as 5.0042 and 14.844 mm, respectively, using RSM. The maximum stress and weight responses of the sandwich structure with optimal design parameters were also found as 83.455 kPa and 2.2667 g. It was revealed that impacts of core height become more noticeable with larger core widths, and they should not be considered separately.