This paper presents a free vibration analysis of functionally graded plates resting on elastic foundation by using a generalized quasi-3D hybrid-type higher order shear deformation theory (HSDT). The displacement field is modeled based on a hybrid-type (hyperbolic and sinusoidal) quasi-3D HSDT with six unknowns in which the stretching effect is taken into account. The elastic foundation follows the Pasternak (two-parameter) mathematical model. The governing equations are obtained through the Hamilton’s principle. These equations are then solved via Navier-type, closed form solutions. The fundamental frequencies are found by solving the eigenvalue problem. The performance of the present theory is demonstrated by comparing results with the 3D exact solution and other closed form solutions available in literature.