This article has investigated dynamic response of simply supported beams carrying moving distributed mass or force. A one dimensional finite element based on the both the first shear deformation (FSDT) and the Classical Laminate beam (CLT) theories is assumed for beam model. A ten degree of freedom beam element for FSDT theory and six degree of freedom element for CLT theory is considered for the beam and the moving distributed mass. Combination of the element property matrices for the moving distributed mass or force and the associated overall property matrices for the beam itself determines the overall effective property matrices of the entire vibrating system. After deriving the governing equations of motion of the beam and the moving distributed mass, the corresponding equations of motion are integrated by applying the Newmark's time integration scheme to obtain the system responses in each time step. Analysis, in its general form, may well be applied to various boundary conditions. However, results from computer simulation are for simply supported beams. The numerical results of free vibration and moving force problems analysis of the beams are presented and, whenever possible, compared to the available analytical solution and other numerical results in order to demonstrate the accuracy of the present method. Effect of Coriolis and centrifugal forces induced by the moving distributed mass and also friction force between the beam and the moving distributed mass are investigated. Numerical results reveal that all above mentioned parameters have significant influence on both the vertical and the horizontal deflections of the inclined beam except the frictional force that can be neglected.