This paper presents a numerical scheme for fluid-structure interaction, especially for flexible structures. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used for the fluid, and a finite element method with Euler beam elements is used for the flexible plate. The direct forcing scheme of the lattice Boltzmann method was improved for the immersed boundary scheme by introducing the occupation ratio of fluid lattices among the interpolated lattices. We compared the results of our proposed scheme with the known results of conventional schemes. Using the proposed numerical scheme, the flow around the flexible plate in a free stream is simulated for the effect of flexibility. Our results show that the major role of the flexibility of the flexible plate is the reduction of the resistance from flow. From the unsteady flow around a flexible plate, we found that the St of the flexible plate up to Re < 80 increased regardless of plate flexibility, but the St in the range of Re > 120 was dependent on plate flexibility. In the range of Re > 120, the St of very flexible plate increased with increasing Re, while the St of rigid plate decreased with increasing Re.