With the great increase of resolution capability of modern sensors, the object is regarded as an extended one with object extension, instead of a point target. Thus, conventional point target modeling and state estimation approaches are no longer suitable for many current tracking scenarios. An extended object's motion and extension (i.e., shape and orientation) undergo an abrupt change when it maneuvers, and both of them are usually highly coupled. In view of this problem, the uncertainties of the extended object maneuvers, the evolution of the kinematic state and object extension, and their close coupling are researched. A general hybrid system modeling framework of the maneuvering extended objects is established. The results show that a joint kinematic state and object extension estimation algorithm can be derived easily owning to the concise linear form of the proposed model. Simulation results and performance comparison demonstrate the effectiveness of the proposed modeling and tracking approaches.