The laser characteristics of laser-diode end-pumped Yb:YAG/Cr 4+ :YAG composite ceramics microchip passively Q-switched lasers were studied by solving the coupled rate equations numerically taking into account the reabsorption of Yb:YAG ceramics at laser wavelength. Effects of the reflectivity of the output coupler, the concentrations and thickness of the saturable absorbers, and pump beam area on the laser performance were investigated analytically. The simulation results of the Yb:YAG/Cr 4+ :YAG composite ceramics passively Q-switched microchip lasers were in good agreement with the experimental data. Better laser performance (high peak power, short pulse width and good optical-to-optical efficiency) of the composite Yb:YAG/Cr 4+ :YAG ceramics passively Q-switched laser can be obtained by using a thin Cr 4+ :YAG ceramic with high concentration, suitable reflectivity of the output coupler and proper pump beam diameter under high pump power intensity according to our simulations.