In the talk, I will report our recent study on the plane Couette flow of a rarefied gas between two moving parallel infinite plates. In case of the Maxwell molecule collisions, we establish the existence of spatially inhomogeneous non-equilibrium stationary solutions to the steady problem for any small enough shear rate. The result indicates the polynomial tail at large velocities for the stationary distribution. Moreover, the large time asymptotic stability of the stationary solution with an exponential convergence is also obtained through the study of the initial boundary value problem in the framework of perturbation and as a consequence the nonnegativity of the steady profile is justified. This is a joint work with Prof. R. Duan and Prof. T. Yang.