The asymptotic theory of Rayleigh shear flow for large values of time is developed on the basis of the linearized Boltzmann-Krook equation. Asymptotic equations for mean velocity outside the Knudsen layer are obtained by employing the Hilbert expansion. Slip boundary conditions are derived from the analysis of the Knudsen layer adjacent to the wall. A solution of the asymptotic equation is obtained under the slip boundary condition and zero initial condition. Discussions are also made of the flow induced by a slowly oscillating flat plate.