In order to obtain the dynamic response of a beam subjected to a moving mass, Its numerical model of spacetime finite element method was established. Considering the inertial terms of a travelling mass, the timevaries different equation of beam under a mass was presented by using. the spacetime finite element method. The characteristic matrices of the discrete element of the BernoulliEuler beam carrying concentrated mass like spacetime inertia and stiffness matrices. Numerical examples by comparing with the results the dynamic response of the beam under the moving mass and the Classical time integration schemes like Newmarkβ and Wilsonθ prove the simplicity and efficiency of the method.