Flow of rarefied gas over an infinite plane wall on the basis of a relaxation model of the Boltzmann equation is considered. The solution is obtained in the form: Hilbert solution and boundary layer term which is appreciable only in a thin layer (with thickness of order of the mean free path) adjacent to the boundary. The Hilbert part dominates in the region away from the boundary. Using the result the asymptotic behavior (for small mean free path) of plane compressible Couette flow is investigated.