Objective: Rate equations model has been formulated to simulate the simultaneous generation of two passive Q-switching pulses using one active medium. It is possible to separate them and employ each pulse in practical applications. Methods: The model was solved numerically by used Rungkutta-Fahelberg method. This model was tested in the study of the effect of saturable absorber ( Cr +4 : YAG ) ions concentration on the duration, energy, and power of the dual pulses which are generation by passive Q-switching of Nd +3 : YAG. Finding: The results of the numerical solution showed that the temporal behavior of photons density of passive Q-switching pulses and the population inversion density of active medium is good agreement with studies which dealt the theory of passive Q-switching, which enhances reliability using this model. Novelty: The mathematical model included six rate equations instead of three or four rate equations. It is based to simulate the 4 F 3/2 , 4 I 11/2 , 4 I 9/2 spectrum lines as a 4-level and 3-level energy schemes of Nd +3 : YAG active medium to get two passive Q-switching laser pulses at the same time (instantaneously) instead of one pulse. Can be separated into two pulses to employ each of them in applications.