Abstract: The boundary displacement in the unsteady Couette flow stage of Newtonian fluid is investigated in this paper. The top wall is always kept stationary and a constant velocity or a sudden constant tangential surface force is imposed on the bottom wall. The fluid velocity distributions are obtained by solving the problems. The time periods for the flow to reach the steady state under different situations are obtained by using the asymptotic analytic method. Then the boundary displacements in the unsteady stage are obtained from the time periods and the boundary velocities. With the shear stress on the inner surface of the bottom wall and the boundary displacements, the work done by the Couette system under different situations is obtained. From the increase of the fluid kinetic energy, the energy dissipations caused by the viscous friction in the unsteady Couette stage are obtained.