A theoretical model for the passively Q-switched (PQS) operation which includes the spatial overlapping between the pump and lasing modes under the thermal lensing effect is developed to give a transcendental equation that can directly determine the critical parameters such as pulse energy, pulse repetition rate, and pulse width for the PQS performance. More importantly, an analytical function which gives the approximate solution for the transcendental equation as well as a specific critical criterion for good PQS operation are derived for practical analyses and design. A Nd:YVO4/Cr4+:YAG system with a concave-convex resonator which can achieve fairly stable PQS pulse trains even at a high pump level is further exploited to manifest the proposed spatially dependent model. The good agreement between the experimental results and the theoretical predictions is verified to show the feasibility of the proposed model for designing high-power PQS lasers with high accuracy.