In this study, a modal superposition approach was adopted to derive the dynamic response of coupled vehicle and bridge systems. The train comprises a number of railway cars, each of which is modelled with ten degrees of freedom. The railway bridge was represented by a simply supported beam modelled as Euler-Bernoulli beam. In the numerical simulations, dynamic responses at the mid-span of the bridge and dynamic responses of the train under different train speeds are computed with random and non random rail irregularities. Effect of parameters like the depth and the position of the imperfection on the rail are taken into account. The coupled system of equations is integrated numerically by the newmark's beta method. The results obtained show that the rail irregularities affect the vertical acceleration of the train, which serves as a measure of the riding comfort of the trains moving over a bridge.