This paper presents the results of an analytic and numerical investigation of flexural vibration of a finite plate clamped to an infinite baffle in mean flow. Attention of the present paper is focused on: (1) the physical mechanisms that lead to unstable conditions for a clamped plate in mean flow; (2) the effects of mean flow, plate aspect ratio and length to thickness ratio, and the structural nonlinearities on the instabilities; and (3) the onset of bifurcation and chaos in plate flexural vibration beyond critical mean flow speeds. In carrying out these analyses, the plate flexural displacements are solved by the Galerkin method. The critical mean flow speeds are determined by a general stability theory and the Routh algorithm. Results show that the instabilities of a baffled plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. The added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of a plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibria. When the mean flow speed exceeds the critical values, the plate may be unstable around all equilibria, jumping from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic. This chaotic behavior disappears, however, when viscous damping is introduced. Accordingly, the plate settles down to a “buckled-down” position owning to the hydraulic fluid-loading effect.