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This article presents the combination of mixed interpolation of tensorial components technique of triangular elements and the edge-based smoothed finite element method (ES-MITC3) developed on the higher-order shear deformation theory (HSDT). The free vibration behavior of auxetic honeycomb sandwich plates with the functionally graded material (FGM) skin layers generated by the proposed program is trained and predicted by an artificial neural network (ANN) model using Matlab coding for reducing computational time and saving computer resources, the proposed approach is expected suitable for practical engineering problems. The strain field of edge-based smoothed triangular elements is approximated by using the generalized C0-HSDT and Lagrange shape functions. Ultra-light features of sandwich plates are obtained by using the auxetic honeycomb core layer (negative Poisson's ratio) and reinforced by FGM skin layers. The present results are compared with other published studies to verify the accuracy and reliability. Besides, the ANN model is also built to train obtained results and accurately predict the natural frequency of structures without running the code. Moreover, the effects of parameters such as geometrical and material properties (especially the auxetic parameters) on the free vibration behavior of auxetic honeycomb sandwich plates with FGM skin layers are investigated in detail. • An edge-smoothed FEM employing the HSDT is developed for vibration analysis of auxetic honeycomb sandwich plates. • The proposed ES-MITC3 element combined with HSDT is more accurate than the original MITC3 element. • Influences of geometrical and material properties on the free vibration of auxetic honeycomb sandwich plates are investigated. • An artificial neural network is established to predict the natural frequency of auxetic honeycomb sandwich plates accurately. • The proposed method can be developed to become the FEM benchmark solutions for auxetic honeycomb sandwich plates. [ABSTRACT FROM AUTHOR]