An investigation into the dynamical behaviour of axial force Rayleigh beam traversed by uniform partially distributed moving loads is carried out. The beam is assumed to be Prismatic while the shear deformation, rotatory inertia and damping are taking into consideration. The resulting coupled partial differential equation is solved using finite difference method. Graphs were prepared for the results obtained. It was found that the response amplitude for the moving mass problem is greater than the response amplitude of the moving force problem.