Moving loads have great impact on structures. On one side, concentrated load moving with high speed induces dynamic impact on structures, influencing their working state and service life. On the other side, these vibrations of the bridge caused due to moving load in turn affect the running stability and safety of moving load.Only in case of short span bridges when mass of moving load is comparable to mass of the bridge, moving load is also taken into account to perform dynamic analysis of the bridge. Displacement response to variation in speed of moving load at different damping of the bridge are plotted and compared when deflection is to be considered at different locations on the bridge. It is observed that when concentrated load moves with critical speed, maximum deflection takes place at mid span of the bridge. When damping is taken into account, a point of singularity occurs below which derived governing equation holds good. The effect of mass of moving load on the dynamic response of the bridge is studied and it is concluded that governing equation in both cases, i.e. without considering the mass of moving load and with consideration of mass of moving load, overlap each other.