We perform numerical simulations of rods and spheroids undergoing Jeffery orbits in a variety of shear flows. The numerical simulations are based on the boundary element method, which allows for the accurate modeling of the problem geometry. We compare the period of rotation for spheroids and rods, both far from walls and very close to walls. We find that the wall effects in three dimensions are minimal, even for flow in gaps not much larger than the longest dimension of the particle. We also show that two‐dimensional simulations grossly overpredict the wall effects seen in three dimensions. Results are similar for both linear and nonlinear shear flows. We also briefly look at the orbital motion of a particle in close proximity to another particle, and show that, again, there is very little effect on the period of rotation, although the resulting centroid trajectories are very different from that of an isolated particle.