In order to analyze the fluid-structure interaction between a flow and a flexible structure, an algorithm was presented to couple the lattice Boltzmann method (LBM) and the finite element method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e., one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also introduced for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.