In the 1970s, it was reported that there were approximately 3700 track kilometers of timber railroad bridges in the United States and Canada. For short spans, they offer an attractive alternative to other types of bridges, as they are economical, faster to construct, and easy to maintain. Current design practices do not allow an independent consideration of the effects of the dynamic loads in sizing the bridge components, because very little information is available on the subject. Dynamic tests were carried out in 1986 on timber bridge spans at two test sites using test trains consisting of a locomotive unit, two loaded hopper cars, and a caboose. This paper gives a brief description of the analytical approach employed for determining the dynamic response of timber bridge spans under railway vehicles travelling at a constant speed. The model comprises a multi-degree-of-freedom system with each vehicle having bounce, pitch, and roll movements. Two parallel chords, each having its distributed mass lumped at discrete points, were used to idealize the bridge spans. A computer program developed on this basis was used to predict the loads at the wheel–rail interfaces and the vertical displacements at the discrete points on the spans. The predicted loads at wheel–rail interfaces and the maximum vertical displacements were found to be in agreement within about 20% and 16% respectively of the measured values. The program was utilized to study the effect of speed and other factors on the dynamic response of open-deck and ballast-deck bridges.Key words: analytical approach, timber railway bridge, railway locomotive and cars, constant speed, wheel–rail interface, loads, displacements, accelerations, dynamic response.