Sandwich panels with cellular material cores are widely used in the aerospace, automotive, and marine industries. Although honeycombs with hexagonal cells are the most frequent shapes for cores, new possibilities in lightweight structures have lately emerged. The present work evaluates the transverse shear modulus of the glass‐reinforced polymer honeycomb core (GFRP ‐ HC) and glass‐reinforced polymer corrugated bioinspired model (GFRP ‐ CBIM) core. The experimental results from the alternative dynamic technique agreed well with the numerical simulation. In the GFRP sandwich beam with corrugated HC and CBIM's core, numerical free vibration analysis was performed. The CBIM core has a higher natural frequency than the HC core, according to the numerical data. Further, numerical analysis has been performed on the bioinspired cores by varying the side length and edge radius. Modified bioinspired model ‐ 03 core design (MBIM03) appears to be a good option for regular honeycombs used in sandwich composite panels for industrial applications that demand low weight, high rigidity, and a large amount of energy‐absorbing capacity.