Master of Science / Department of Mechanical Engineering / Warren N. White / The subject of linear control is a mature subject that has many proven powerful techniques. Recent research generally falls into the area of non-linear control. A subsection of non-linear control that has garnered a lot of research recently has been in underactuated dynamic systems. Many applications of the subject exist in robotics, aerospace, marine, constrained systems, walking systems, and non-holonomic systems. This thesis proposes a sliding mode control law for the tracking control of an underactuated dynamic system. A candidate Lyapunov function is used to build the desired tracking control. The proposed control method does not require the integration of feedback as does its predecessor. The proposed control can work on a variety of underactuated systems. Its predecessor only worked on those dynamic systems that are simply underactuated (torques acting on some joints, no torques acting on others). For dynamic systems that contain a roll without slip constraint, often a desired trajectory to follow is related to dynamic coordinates through a non-holonomic constraint. A navigational control is shown to work in conjunction with the sliding mode control to allow tracking of these desired trajectories. The methodology is applied through simulations to a holonomic case of the Segbot, an inverted cart-pole, a non-holonomic case of Segbot, and a rolling wheel. The methodology is implemented on an actual Segbot and shown to provide more favorable tracking results than linear feedback gains.