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Abstract: This paper presents computational analysis of a fluid–structure interaction for a flapping flexible plate moved with propulsive velocity in quiescent fluid to investigate the effect of flexibility on propulsive velocity, which is critical for fish, birds, insects, and micro air vehicles with flapping wings. This study found that the mechanism of the flapping plate moved with propulsive velocity differs from that of the plate fixed in the propulsive direction, and the flexibility of the plate improves the propulsive velocity to create an optimal propulsion. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used to simulate the fluid, while the finite element method with Euler beam elements is used to model structural deformation of the flexible plate. We developed the moving domain scheme to reversely move the domain at the velocity of the plate to simulate the moving plate. [Copyright &y& Elsevier]