The estimation of dynamic responses of a bridge under vehicle loads moving along the bridge is frequently a problem of great interest for bridge engineers. Presented herein is an analytical approach to estimate the dynamic responses of a simply supported Euler-Bernoulli bridge under a set of vehicle axle loads moving along the bridge at constant speed. The approach involves convolution of the vehicle axle loads with modal responses of the bridge. The convolution integral is solved in time domain by a numerical integral approach. The solution was verified and good agreement was found.