The dynamic behaviour of a finite beam subjected to travelling loads with acceleration is investigated. The velocity of the load is assumed to be ( v0 + βt), where v0 and β are the initial velocity and acceleration, respectively, and both of them are constants. The fundamental equation of motion of the beam is obtained by the energy method. The integrations involved are calculated by using Fresnel integrals. From the results of the theoretical analysis, it became evident that the dynamic behaviour of the beam is affected remarkably by acceleration.