Mobility Model has drawn more and more attentions since its critical role in Mobile Wireless Networks performance evaluation. This paper analyzes the mobility patterns in the catastrophe rescue scenario, and proposes the Random Waypoint with Base Point mobility model to model these characteristics. We mathematically analyze the speed and spatial stationary distributions of the nodes and derive explicit expressions for the one dimensional case. In order to keep the stationary distribution through the entire simulation procedure, we provide strategies to initialize the speed, location and destination of the nodes at the beginning of the simulation. The simulation results verify the derivations and the proposed methods in this paper. This work gives a deep understanding of the properties of the Random Waypoint with Base Point mobility model and such understanding is necessary to avoid misinterpretation of the simulation results. The conclusions are of practical value for performance analysis of mobile wireless networks, especially for the catastrophe rescue scenario.