We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two parallel plates when one of them moves in its own plane. The boundary conditions are assumed to be of the "bounceback" type and the molecules to be Maxwelrs. Under this condition the moments can be computed exactly, following a method used by Ikenberry and Truesdell in the unbounded case. This allows a comparison of the Monte Carlo methods with the exact solution and an evaluation of its accuracy.