The vibration response including displacement, velocity and acceleration of the elastic body under the action of the moving load and moving mass is analyzed in this study. First, the effect of the moving speed and object mass on the vibration displacement of a beam with simple supports is calculated. The vibration displacement of the beam with and without considering the inertial force of the moving object is compared. Then, in terms of the difficulty in convergence of the vibration acceleration when using the Newmark-β method, the generalized Hilber-Hughes-Taylor-α (HHT-α) method is adopted to calculate the acceleration, and the influence of the amplitude decay factor γ on the vibration response is investigated. Finally, an engineering practical method for computing the vibration of the general elastic body under moving load is introduced by extracting the mass matrix and stiffness matrix from the finite element solver. It is found that the inertial effect of the moving object plays a significant role when the object mass is large especially under high-speed motion condition. Increasing the parameter γ in HHT-α method helps to achieve convergence for vibration acceleration accompanied by numerical dissipation, while the Newmark-β method is still reliable in analyzing the displacement and velocity of the elastic body as these two vibration parameters are not easily divergent, and the variation tendency and vibration amplitude of the displacement and velocity are less affected by the parameter γ. This research offers valuable guidance for investigating the dynamic behaviour of elastic structures subjected to a moving object.