The Large Synoptic Survey Telescope is a complex hardware - software system of systems, making up a highly automated observatory in the form of an 8.4m wide-field telescope, a 3.2 billion pixel camera, and a peta-scale data processing and archiving system. As a project, the LSST is using model based systems engineering (MBSE) methodology for developing the overall system architecture coded with the Systems Modeling Language (SysML). With SysML we use a recursive process to establish three-fold relationships between requirements, logical & physical structural component definitions, and overall behavior (activities and sequences) at successively deeper levels of abstraction and detail. Using this process we have analyzed and refined the LSST system design, ensuring the consistency and completeness of the full set of requirements and their match to associated system structure and behavior. As the recursion process proceeds to deeper levels we derive more detailed requirements and specifications, and ensure their traceability. We also expose, define, and specify critical system interfaces, physical and information flows, and clarify the logic and control flows governing system behavior. The resulting integrated model database is used to generate documentation and specifications and will evolve to support activities from construction through final integration, test, and commissioning, serving as a living representation of the LSST as designed and built. We discuss the methodology and present several examples of its application to specific systems engineering challenges in the LSST design.