The governing equation of an axially moving plate on simple supports is derived. The differential quadrature method is employed to analyze the natural frequencies and critical speed of the plate under in-plane loading. The contribution of the axially moving speed, plate stiffness and length-width ratio is discussed. It is concluded that the increasing axial speed leads to decreasing of natural frequencies while the stiffness causes higher values of natural frequencies. When the length-width ratio is small enough, the axially moving plate can be studied by beam model.