In this paper the effect of the ratio of active medium effective beam area to the saturable absorber effective beam area (A/As) on absorption activity of saturable absorber hase been studeid . Fiber doped by thulium used as a active medium , whil Cr+4:YAG used as a saturable absorber .For simulation the system, rate equations model hase been solved numerical using Runge-Kutta-Fehalberge method. The simulation show the absorption activity of each level in SA reaches to converging in value and the optical bleaching state occurs at advanced time with the increase of A/As .