Friction is a difficult phenomenon to model and simulate. One promising friction model is the LuGre model, which captures key frictional behavior from experiments and from other friction models. While displaying many modeling advantages, the LuGre model of friction can result in numerically stiff system dynamics. In particular, the LuGre friction model exhibits very slow dynamics during periods of sticking and very fast dynamics during periods of slip. This paper investigates the best simulation strategies for application to dynamic systems with LuGre friction. Several simulation strategies are applied including the explicit Runge–Kutta, implicit Trapezoidal, and implicit Radau-IIA schemes. It was found that both the Runge–Kutta and Radau-IIA methods performed well in simulating the system. The Runge–Kutta method had better accuracy, but the Radau-IIA method required less integration steps.