An investigation into the dynamic behaviour of Viscously damped Rayleigh beam traversed by a uniform spatially distributed moving masses is carried out. The beam is assumed to be prismatic while the effects of two kinds of pressure are considered, that is the moving load and moving force. The pertinent governing partial differential equations, the boundary and initial conditions were analyzed by a series solution in terms of the normalized deflection curve of the beam and the unknown functions of time. This resulted into a set of coupled ordinary differential equations which are numerically solved by the finite difference scheme with the aid of a Visual Basic 6.0 programme. It was observed that the response amplitude of a Rayleigh beam due to moving mass increased as mass and length of the load increased, whilst the amplitude was found to reduce with increasing time. It was further observed that the response amplitude due to moving force was greater than the response amplitude due to moving mass.