To investigate the vibration of simple beams subjected to the passage of high speed trains, a train is modeled as the composition of two subsystems of wheel loads of constant intervals, with one consisting of all the front wheel assemblies and the other the rear assemblies. By an analytical approach, the key parameters that govern the dynamic responses of the beams are identified, using the moving load assumption. To evaluate the inertia effect of moving vehicles, numerical solutions are obtained using Newmark's β method. Based on the condition of resonance and the condition of cancellation for the waves generated by continuously moving loads on the beam, optimal design criteria that are effective for suppressing the resonant responses are proposed. In designing a high speed railway bridge, such criteria should be considered in selecting the span length and cross-section of the beam, given the car length, axle distance and operating speed of the train.