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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.