This research examines the vibrational characteristics of simply supported functionally graded porous plates. Higher-order non-polynomial theory and transverse shear effects are analyzed as a function of plate thickness. Without a coefficient for shear correction, the existing model has merely four unknown variables. The Hamiltonian model is utilized to formulate the equations of motion. The solutions are obtained by Navier’s technique, followed by the determination of fundamental frequencies by the resolution of a system of eigenvalue equations. The findings of this analysis are given and compared with existing literature.