•The single layer type HSDT kinematic applicability is verified for skew sandwich.•The FE eigenvalues are predicted considering the drilling degrees of freedom.•The numerical model accuracy is verified with experimental comparisons.•The fabricated specimen experimental properties are implemented for the analysis.•The inevitability of HSDT type model is established from the current analysis. The experimental eigenvalue responses of the epoxy-filled skew sandwich structure are computed first-time in this research to show the suitability of equivalent type single-layer higher-order theory (including through-thickness stretching term effect) for the analysis. The sandwich shell model is formulated mathematically for the variable geometrical configurations considering the effect of skew angles. Further, the motion equation of the vibrated structure is solved numerically with the advent of the linear isoparametric finite element technique. Firstly, the numerical solution accuracy is established by verifying the modal values with the already published data including their element sensitivity test. Also, a few experimental frequencies (first-five mode) are recorded (impact type vibration analyzer) using the in-house fabricated sandwich plate components considering the experimental material properties for the comparison purpose. Moreover, a simulation model is prepared using the commercial package to show the efficacy of the presently proposed single layer theory for the analysis of the sandwich structure with and without the skew angle effect. The present comparison indicates that the proposed equivalent single-layer model is capable of solving the modal responses considering different structural input parameters (number and stacking sequences of the face sheet layers and variable aspect/thickness ratios) with adequate accuracy. Lastly, the verified model is explored to show its applicability by solving different numerical examples due to the change in their basic input parameters affecting the geometry, material properties and the stiffness.