Shaqfeh and Fredrickson [Phys. Fluids A2, 7 (1990)] renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension,nl3≫1 and &fgr;≪1, where &fgr; is the fiber volume fraction,nis the number of fibers per unit volume, andlis the fiber half‐length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to theO(&ggr;˚) Jeffrey rotation rate [Proc. R. Soc. London Ser. A102, 161 (1922); J. Fluid Mech.14, 284 (1962)] due to hydrodynamic interactions is shown to beO[&ggr;˚/ln(1/&fgr;)], where &ggr;˚ is the shear rate.