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In this article, the non‐linear free vibration behavior of sandwich composite panels with sinusoidal corrugations is examined. These panels consist of a top and bottom skin made of a graphene‐reinforced composite, with an auxetic honeycomb core having negative Poisson's ratio. The non‐linear kinematic field is based on Kant's higher‐order shear‐deformation theory and the Green‐strain, which incorporates all the higher‐order terms. By implementing the Hamilton principle, the non‐linear governing equations are affirmed and solved further through 2D‐isoparametric finite element approximations via Lagrangian elements in conjunction with Picard's successive iterative scheme. The comparison and validation tests demonstrate the correctness of the present model. The established sandwich model is further employed for various parametric conditions by varying the core‐to‐face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non‐linear frequencies at small‐to‐large amplitudes for the sandwich shell structures and are discussed in detail. In addition, a multi‐objective parametric optimization is conducted using the response surface method to investigate the optimal values of the corrugated auxetic honeycomb shell panel's parameters, resulting maximum frequency. Highlights: Non‐linear vibration of corrugated sandwich shell panel.Graphene reinforced skins and honeycomb auxetic core.Kant's higher‐order shear‐deformation theory and Green‐Lagrange non‐linearity.Hamilton principle and Picard's successive iterative scheme.Multi‐objective parametric optimization and prediction using response surface methodology. [ABSTRACT FROM AUTHOR]