To combine the advantage of the IBM for its simple boundary treatment and that of the LBM method for its fast flow simulation,hybrid methods coupling these two approaches have been developed recently. Among the various IBMs, Peskin’s diffuse boundary approach is particularly suitable for this combination, since in this approach all the grid points within the computational domain are treated with a unified equation. The standard LBM utilizing a uniform Cartesian mesh was first combined with the IBM for handling the rigid moving particles by Feng and Michaelides. After that, several versions of IBLBM have been developed for the flow involving rigid bodies. More recently, the IBLBM has been extended to the simulation of elastic membranes and plates, including both two and three dimensions.