This thesis examines the use of model-based systems engineering techniques to analyze search and rescue (SAR) operations. It first provides background on SAR organization and procedures as outlined in the U.S. National SAR Plan. It then develops a design reference mission involving man overboard and downed aircraft scenarios. Various modeling techniques are applied to the mission, including sequence diagrams, IDEF0 diagrams, hierarchy charts, and the Monterey Phoenix modeling language. The models provide insights into critical system behaviors and interactions within the SAR process. The study demonstrates that multiple modeling iterations across different techniques are needed to fully capture the complexities of SAR system design and execution.