This study is devoted to the investigation of dynamic analysis of a bridge supported with many vertical supports under a moving load. Each vertical support is modelled as a linear spring and a linear damper. The analysis is based on Euler-Bernoulli beam theory. The present method utilises the concept of distributed moving load, spring force and damping force, and avoids the use of matching conditions. Expressing these forces in tenus of the unknown function of the problem, it highly simplifies obtaining an exact solution. An important property of Dirac delta distribution function is utilised in order to reach the exact solution. Considering one and three vertical supports, the response of the supported bridge is plotted and compared to different values of parameters. In the case of an undamped bridge with no support, the results are compared with those of previous papers.