The dynamic response of a girder bridge under trains is studied with an emphasis on the vertical track acceleration. The vehicles are modelled as a series of moving loads. The efficiency of the method is demonstrated on the simply supported railway bridge of the length Lb = 38m subjected to the series of the bogie forces of the conventional IC train. The closed-form solution of the bridge response with the intention to resonance and cancellation effects is applied. The acceleration response is investigated for the resonance train speed c = 65 m/s = 234 km/h, considering the modes of vibration j = 1 and j = 1+3, because higher modes can have significant influence on the acceleration amplitude. The limits of acceleration due to the ballast stability and the traffic safety are evaluated.