The transverse vibration of an axially moving elastic beam supported by verticalspring boundary under external excitation was studied. By using the generalized Hamilton principle, the governing equation of motion was obtained. Moreover, the modal analysis was conducted by using analytic method, and the relationship between natural frequency and axial velocity was revealed. The expression of the critical velocity of the axially moving beam was derived, and the effect of the spring stiffness on the critical velocity was studied. The critical velocity converges to a certain value with the increase of the spring stiffness. Furthermore, the amplitudefrequency responses in steady state were obtained by using the Galerkin truncation method. The vibration isolation performances of the system were evaluated by the force transmissibility. There are multiple peaks of the force transmissibility under highfrequency external excitations.