In this paper, an effective unified numerical approach is utilized to analyze the free and forced vibration response of two-directional functionally graded (2D-FG) thick circular and annular plates with variable thickness. The material properties are assumed to be graded continuously both in thickness and radial directions. The governing equations are converted to a set of ordinary differential equations (ODEs) based on the first order shear deformation theory. Obtained canonical equations are solved numerically by the Complementary Functions Method (CFM) combined with the Laplace transform for the first time. Using an effective and suitable inverse numerical Laplace transform method, the results are transferred back to time space. The damping model of Kelvin is used in the damped forced vibration analysis. The novelty of this paper is to infuse this efficient and accurate method to the dynamic analysis of a wide range of solid circular or annular plates, with linear or non-linear thickness profiles, radially Functionally Graded (FG), FG in the thickness direction or 2D-FG, without any restrictions. The influence of material variation exponents and thickness profiles on the considered problems are investigated. Several examples are presented and results are verified with those obtained by finite element method and available published literature. Excellent agreement is observed.