In this paper, a spatial dynamic analysis model for the train-bridge system under random excitations was established. The random excitations were analyzed and generated by the time series autoregressive model from the experimentally measured wheel accelerations. The whole histories of the train running on the bridges were simulated on computer. The responses of bridges were calculated and statistically studied. Based on the calculation results, the reinforcement schemes for steel girders were designed and some of them were applied to real bridges. The field-tests were carried out before and after the bridge reinforcement. The measured data from the tests proved the effectiveness of the reinforcement schemes. (C) 2001 Elsevier Science Ltd. All rights reserved.