In this article, the dynamic behavior of the bridge under the effect of the moving vehicle is analyzed using the theory of first-order shear deformation or Timoshenko's theory. The bridge and the vehicle are considered as a multi-layer composite beam and a half-car, respectively. The governing equations of the beam and the vehicle have been derived using the finite element method. In the finite element method, the three-node high-order beam element was also used. Solving the time-dependent equations has been done using the linear Newmark method. The number of degrees of freedom of the vehicle is also two degrees of freedom. In order to extract the results, the couplings of bending-tension, bending-torsion and torsion-tension, together with the effects of shear deformation, rotational inertia and Poisson's effect have been used. The results of the free and forced vibration of the bridge and vehicle system are in acceptable agreement with the results of other articles and the commercial software of COMSOL.