Modern structures and components may require advanced materials whose properties vary continuously not only in one specified direction, but also different other directions. In particular, the bi-directional functionally graded materials (2D-FGMs) introduced are expected to have more effective properties, consequently eliminating commonly awkward problems such as local stress concentrations and delamination. In this paper, buckling and bending behaviors of 2D-FGM plates, which are of great importance in the design and development of engineering applications, are numerically analyzed by a finite element model. The plate kinematics are described using a new third-order shear deformation plate theory (TSDT), without the need for special treatment of shear-locking effect and shear correction factors. The present TSDT theory based on rigorous kinematic of displacements, which is shown to be dominated over other preceding theories, is derived from an elasticity formulation, rather by the hypothesis of displacements. The materials are assumed to be graded in two directions and their effective properties are computed through the rule of mixture. The accuracy of the proposed approach assessed on numerical results is confirmed by comparing the obtained results with respect to reference published solutions. The effects of some numerical aspect ratios such as volume fraction, boundary conditions, thickness to length ratio, etc. on static deflections and critical buckling are numerically studied. The investigation of results confirms that such aforementioned aspect ratios have significant effects on the mechanical behaviors of plates.