We use Brownian dynamics and slender-body theory to simulate suspensions of rigid fibers under simple shear and pressure-driven flow between two parallel walls at zero Reynolds number and high Peclet number. The suspended fibers interact hydrodynamically with the bounding walls as well as with other fibers in suspension. We also extend the theory for cross-stream migration of a rigid fiber near a wall (Park, Bricker and Butler, Phys. Rev. E 07) and compare with the results of the simulations. The center of mass distributions obtained by simulations and the theory are in good agreement and show a net migration away from the wall. The good agreement validates approximations made in the theory, such as negligible effect of the wall on the orientation distribution. (Supported by NSF CAREER Award CTS-0348205)