Objective: Mathematical model of rate equations was proposed to simulate the performance of laser system to generate passive Q-switching laser pulse, which interacting with Raman medium to produce Stokes and anti-Stokes pulses. Methods: The proposed rate equations model has been tested theoretically in optical system consist of Nd:YVO 4, PbWO 4, andCr +4 :YAG as active medium, Raman medium, saturable absorber material respectively. Rung-Kutta-Fehelberg numerical method used in the solve of the model. The results were showed good compatibility compared with those of previous studies. After performance the verification steps, this model was tested in the study of the effect of saturable absorber ions concentration on the characteristics of passive Q-switching, Stokes, anti-Stokes pulses. Findings:The proposed rate equations model it is possible adopt in theoretical studies related to high power pulses interaction with Raman medium to generate Stokes and anti-Stokes pulses. Novelty: Add new mathematical equations and terms to that of previous mathematical models. The models consist of six equations instead of four or five equations.