In this study, the dynamic response of non uniform Rayleigh beam resting on Pasternak foundation and subjected to concentrated loads travelling at varying velocity with simply supported boundary condition has been investigated. Analytical solution which represents the transverse displacement response of the beam under both concentrated forces and masses travelling at non uniform velocities was obtained. To obtain the solution of the fourth order partial differential equation with singular and variable coefficients, a technique based on the Generalized Galerkin’s Method and the struble’s asymptotic technique was employed. Numerical results in plotted curves are presented. The results show that as the Rotatory inertia increases, the response amplitudes of the non uniform Rayleigh beam decreases for both moving force and moving mass problems. Furthermore, the results show that the response amplitudes of the non uniform Rayleigh beam decreases with an increase in the values of the shear modulus 0 G for fixed values of foundation modulus 0 K and Rotatory inertia . Similarly, as 0 K increases, the response amplitudes decreases but the effect of 0 G is more noticeable than that of . 0 K Finally, the critical speed for the moving mass problem is reached prior to that of the moving force for the non uniform Rayleigh beam problem in the illustrative example considered. Hence, the moving force solution is not a safe approximation to the moving mass problem, therefore, we cannot guarantee safety for a design based on the moving force solution since resonance is reached earlier in the moving mass problem than in the moving force problem.