In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton's principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin's method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM) with ANSYS software, the obtained results in nonlinear form are verified by FEM results. Then, a parametric study is conducted by changing the size of moving mass/force and the velocity of the traveling mass/force with a constant acceleration/deceleration, and the outcome nonlinear results are compared to the results from linear solution.