We investigate the unsteady flow of a discrete gas between two infinite moving and impermeable parallel plates. The first studies of the Couette flow problem in the scope of discrete kinetic theory were carried out in the steady case with discrete models having only one speed (Broadwell J. E., 1964). Only the behavior of the total density and the mean velocity has been examined. In the unsteady case, a work carried out with a class of four velocity models with the same modulus made it possible to study the evolution of total density, tangential and normal velocities as functions of time (Gatignol R., 1979). The objective of the present study with a ten velocity discrete model with two different speeds (d'Almeida A. and Gatignol R., 1995), is to study the transition from unsteady flow to steady flow by analyzing the behavior of the macroscopic variables of the flow (total density, kinetic temperature, normal and tangential velocities). The problem is solved numerically using the fractional step method. By varying the Knudsen number Kn, we pass from continuous flows to rarefied flows. The study therefore focus on finding and evaluating the effects of rarefaction highlighted by other methods of investigation and analyzing their evolution with time.