The interaction with axial flow can significantly alter the mechanical behavior of plates in qualitative and quantitative terms. A numerical method is presented for the dynamic stability analysis of plates subjected to uniform axial flow, which can serve as a general analysis tool for the positively supported plates within linear theory. The plate response is described in the modal space that the corresponding perturbations in the flow field are expressed by means of modal components of the assumed velocity potential field. The modal characteristics of the plate are identified by adopting the heterosis finite element over the Mindlin theory; the fluid action on the plate is computed through a higher-order boundary element solution of the flow problem. The plate-flow interaction is represented in terms of added mass, fluid damping, and fluid stiffness effects. The plate-flow system acts as either gyroscopic conservative or non-conservative, based on the support conditions of the plate leading and trailing edges. The method is applied on two sets of problems that involve rectangular plates in open and confined flow-its performance, accuracy, and adaptability are assessed and the dynamic behavior and stability characteristics of supported plates in axial flow are investigated.