This thesis explores two aspects of modeling the behavior of joint friction in structures. The first aspect deals with the accurate and efficient simulation of a simple system that incorporates the LuGre friction law. Energy transfer and dissipation in a structural joint model is the second topic of this thesis. It is hypothesized that friction could serve to pump energy from one frequency to higher frequencies where it might be dissipated more quickly. Motivation for this study stems from the need to have accurate models of high-precision space structures. Because friction at connecting joints plays a major role in the damping capacity of the structure, a good understanding of this mechanism is necessary to predict the vibratory response and enhance the energy dissipation of the structure. Simulation results of a dynamic system with LuGre friction show that the system is relatively well-conditioned when the slip velocity is small, and ill-conditioned for large slip velocities. Furthermore, the most efficient numerical method to simulate this system is determined to be an implicit integration scheme. To study the energy transfer and dissipation, two models of a jointed structure with friction are considered. Results from the steady-state forced responses of the two structural systems indicate that friction converted low frequency, single harmonic excitation to multi-harmonic response through internal resonances. However, differences in energy dissipation results between the models show that the response of a frictional system is highly sensitive to system parameters and friction laws. Conclusions and suggestions for future research are also discussed.