On the basis of the thirdorder shear deformation theory, finite element equation of the axially moving plate is established via principle of virtual work. The solution domain is discreted by applying a fournode quadrilateral element containing nodal deflection, its slope and crosssectional rotation angle. Then the constraint of discrete spring supports is introduced into the finite element equation in the form of potential energy for the first time. In order to prove effectiveness, the present results are compared with those from ANSYS under the conditions of different boundary conditions and different support stiffness. Subsequently, the relationships between the axial velocity as well as spring stiffness and the real and imaginary parts of the complex frequencies are obtained for the axially moving thin plate with two kinds of boundary conditions. It shows that the axially moving plate may be instable with a high velocity, and the vibration frequency increases with a high spring stiffness. Finally, the relationship between the plate thickness and the complex frequency is demonstrated, and the effect of plate thickness on stability of the axially moving thirdorder shear deformation plate is thus revealed.