The behavior of a passive plate placed behind a D-cylinder is numerically studied by using the modified immersed boundary methods. The linear Euler–Bernoulli Beam theory is employed as the structure model for the flexible plate. The effects of the Reynolds number, the mass ratio and rigidity of the material and the distance between the D-cylinder and the plate are investigated. Results show that, the initial perturbation is inhibited when the Reynolds number is small. By increasing the Reynolds number, the larger the Reynolds number the larger amplitude of the plate’s oscillation. When the plate is placed close to the D-cylinder, its surface is surrounded by the vortical layer and there is no vortex shed from the D-cylinder, the ‘attached vortex mode’. The ‘Kármán vortex street’ is formed at the front of the plate when it is placed further behind the D-cylinder, the ‘vortex street mode’. Compared with the effects of Reynolds number, the material parameters do not play a crucial role on the plate’s oscillation behavior. The drag forces which act on the plate are related to the flow structures. When the distance is smaller with S/L=1.5, the plate is located in the suction domain and negative drag acts on the plate initially. For the large distance case, when the incoming shed vortex contacts the plate’s head, a low pressure domain is generated and this results in lower drag. The ‘vortex street mode’ can get more kinetic and strain energy by the plate, since the shed vortices make the plate’s deformation mode more complex and the oscillation frequency is also larger than the one of the ‘attached vortex mode’.