A numerical investigation on the influence of structural flexibility and flow velocity on the flow-induced acoustic and vibration response of a plate is presented. Simulations are performed on a test geometry of rigid square bluff body with a trailing flexible plate in low Reynolds number flow stream. The focus of the study is to characterize the flow-induced vibration and associated aerodynamic far field sound radiation from a flexible structure in flow. The role of flow velocity and level of structural flexibility on the acoustic radiation is thoroughly investigated. A linearized Euler equation based computational aeroacoustic hybrid method and a surface source approach for coupling the flow and acoustic domains are implemented with a bi-directional fluid structure interaction. The vortex shedding frequency of the coupled fluid-structure system synchronizes with the fundamental frequency of the trailing plate and steady-state vibration of the plate is observed. The results indicate that the relation between vibration level and the flow velocity as well as structural flexibility is not linearly related. For a particular combination of flow velocity and plate stiffness, the coupled fluid-structure system shows the resonance condition. The observed resonance frequency is slightly different from the free vibration (natural) frequency of the plate. Computation of the acoustic shows that the magnitude and spectral nature of the far field sound depends on the amplitude of the vibration and a higher acoustic pressure and the sound rich in tones is observed at resonance condition.