Physical systems are by nature continuous. Perceived discontinuities in system models are in reality nonlinear behaviors that are linearized to reduce computational complexity and prevent stiffness in system analysis and behavior generation. Discontinuities arise primarily from component parameter simplification and time-scale abstraction. Discontinuities in models are handled by introducing idealized switching elements controlled by finite state automata to bond graph models. In this paper, we make a systematic study of the nature and effects of discontinuities in physical system models, and present an algorithm that generates consistent and correct behaviors from hybrid models. A primary contribution of this paper is the characterization of discontinuous changes, and a systematic method for validating system models and behavior generation algorithms.