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The Lattice Boltzmann Method (LBM) has been successfully used in various engineering applications in modeling the fluid flow.In this paper,LBM is used to simulate the two dimensional incompressible Couette flow.The numerical solution to the problem of incompressible Couette flow is compared with the well known analytical solution.It is shown that the LBM has a remarkable ability to simulate fluids flow in terms of computational efficiency and stability.