Bridges are vital components of the railroads. High speed of travel, the periodic and oscillatory nature of the loads and the comparable vehicle bridge weight ratio distinguish the railway bridges from the road bridges. On the other hand, there is close proximity between estimations by some numerical methods and the measured data regarding the bridge-vehicle dynamic response under the moving load conditions. This has boosted the confidence in the numerical analysis of the vehicle-bridge dynamics. There is hardly any report regarding the response of the railway bridge under the effect of two trains entering from the opposite directions of the bridge while considering different speed of travel or the train geometrical specifications. It is the purpose of this article to present an analytical method for the dynamic analysis of the railway bridges under the influence of two opposing series of moving loads. The method starts by writing the motion equations for the bridge that interacts with the rolling stock. The concept of modal superposition is used to solve for the system motion equations. A computer program is written in MATLAB environment. It solves for the system motion equations and gives output in terms of bridge deflection. Some case studies are also considered. Validation of the proposed method is done by comparing the results with some analytical and numerical methods that are already available in the corresponding literature. However, the short coming of such methods is that they are applicable only to some limited scenarios. Furthermore, the effects of the parameters such as the distance between the bogies, and the distance between the axles of the bogies are studied. Also, the conditions of resonance and cancellation in the dynamic response for a variety of vehicle-bridge specifications are investigated.