This article presents a different polynomial interpolation function based dynamic finite element model to study and analyze the mechanical behavior of bidirectional functionally graded beams under moving load. To improve the mechanical behavior of the functionally graded beam, material properties are assumed to be symmetrically distributed throughout the axial and transverse directions. The first order shear deformation theory is employed to incorporate the transverse shear strain. To overcome the shear locking phenomena with satisfying all true kinematic constrains and no need to assume new strain field, five noded beam element with ten degrees of freedom and different polynomial interpolation functions is used. Cubic polynomial interpolation functions are assumed for the transverse deflection while quadratic polynomials are used for both axial and rotational displacements. Equations of motion are developed using the virtual displacement principle. Finite elements stiffness, mass matrices and force vector are derived in explicit forms. The unconditionally stable Newmark technique is employed for the transient time response. The developed procedure is checked and compared with the available results and an excellent agreement is observed. The applicability of the developed numerical procedure is demonstrated and discussed. Effects of the geometrical, material characteristics, and the moving load speed on the mechanical behavior are investigated and discussed. Obtained results are supportive for the design and manufacturing of bidirectional functionally graded beam structures.