In this study, the static bending, buckling, and free vibration behaviors of two-dimensional functionally graded (2D-FG) tapered micro/nanobeams are modelled and analyzed. For the first time, the nonclassical equations of motion and corresponding boundary conditions of 2D-FG beam are simultaneously derived in the framework of the modified couple stress and Gurtin-Murdoch surface elasticity theories in conjunction with the Timoshenko beam theory. Here, all the material properties of the beam are graded along the thickness and length directions according to the power-law. Both thickness and width of the beam are considered to vary linearly along the length direction. Unlike existing Timoshenko beam models, the current formulation accounts for the axial and bending deformations, Poisson's effect, and exact position of the physical neutral plane. Differential quadrature method is employed to estimate the variable coefficients of the derived equations. The bending deflection, critical buckling load, and free vibration frequency of simply supported 2D-FG Timoshenko nanobeam are obtained employing the Navier's method. A parametric study is accompanied to investigate the effects of the different material and geometrical parameters on the mechanics of 2D-FG micro/nanobeams. It is observed that these parameters are very important in investigating the static and dynamic responses of 2D-FG micro/nanobeam.