In this paper, various four variable refined plate theories are presented to analyze vibration of functionally graded sandwich (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition and plate geometry, on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of FG plates.