In this paper, the vibrational response of the functionally graded plate has been carried out using non-polynomial based algebraic shear deformation theory. Hamilton’s variational principle has been used in deriving the governing equations. The Navier solution technique has been employed to solve the governing equation in conjunction with boundary conditions which are simply supported. In addition to these, the power-law governing equations have been considered for calculating the effective material properties of FGM and its mechanical properties are considered to be changing in the direction of thickness. The non-dimensional frequency has been evaluated for several vibrating modes of functionally graded thin and thick plates. The frequency parameter has also been evaluated for different aspect ratios and thickness ratios. © Springer Nature Singapore Pte Ltd. 2020.