In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.