Abstract- In this paper, The behavior of an Er-Yb:Glass laser Q-switched with Co²⁺:MgAl₂O₄ saturable absorber is modeled by using the rate equations. This model investigated once in presence of percentage of unpumped active element and once again in presence of completely pumped active element. After analyzing the rate equations, the output pulse width and energy are calculated and finally two cases are compared to each other. The results show that the time of propagation laser pulse in presence of unpumped active element occures later in compare with completely pumped active element.