Simulation results for the motion of flexible fibers modeled as rigid spheres connected by ball and socket joints are presented. Simulations of isolated stiff fibers reproduce such features of Jeffery orbits as orbit stability, the dependence of the dimensionless orbit period on only the fiber aspect ratio (independent of shear rate and orientation), and trajectories identical to those of prolate spheroids of the same equivalent aspect ratio. Simulations of stiff fibers "pole-vaulting" near a bounding surface qualitatively reproduce experimental observations. Fiber trajectories are very sensitive to the short-range interactions between a fiber and a bounding surface. In contrast to rigid fibers, flexible fiber orientations drift in unbounded simple shear and parabolic shear flows. The drift direction and rate depend on fiber stiffness, initial orientation, as well as the ambient how field. A wide variety of configurational dynamics are observed, which also depend on the fiber stiffness, initial orientation, and the ambient flow field. These results agree with previous experimental observations of flexible fibers in shear flows.