There is a need for smaller and more economic transportation systems. Two-wheeled inverted-pendulum machines, such as the Segway, have been proposed to address this need. However, the Segway places the operator on top of a naturally unstable platform that is stabilized by means of a control system. The control stability of the Segway can be severely affected when minor disturbances or unanticipated conditions arise. In this thesis, a dynamic model of a Segway is developed and used in simulations of various conditions that can arise during normal use. The dynamic model of a general two-wheeled inverted pendulum and human rider is presented. Initial estimates of the parameters were calculated or obtained from other references. The results from numerous experiments are presented and used to develop a better understanding of the dynamics of the vehicle. The experimental data was then used to adjust the model parameters to match the dynamics of a real Segway Human Transporter. Finally, the model was used to simulate various failure conditions. The simulations provide a better understanding of how these conditions arise, and help identify which parameters play an important role in their outcome.