Abstract: The first two natural frequencies of transverse vibration of moving vehicles over a smooth road based on a half-vehicle model are numerically simulated. The car's body is modeled as an Euler-Bernoulli beam with free boundary conditions at both ends, and the tires are modeled as two springs with different spring indexes in the half-vehicle model. The governing equation for transverse vibration of the car's body is established. The first two natural frequencies are obtained for the beams via the Galerkin method with both the trial and weight functions chosen as eigenfunctions of a stationary beam under the free boundary condition at both sides. The numerical results illustrate the relation of the first two natural frequencies with the changing speed of vehicle, the flexural stiffness of the car's body and the stiffness of the tires.