A wheeled mobile manipulator system is modeled using Kane's dynamic equations. Kane's equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane's approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints associated with slipping and skidding as well as conditions for avoiding tipping over are included. The resulting equations, along with the set of constraint equations provide a safe and complete framework for developing control strategies for mobile manipulator systems.