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New analytical approximations are proposed for the linear elastic properties of fiber materials with imperfect interfacial bondings, across which displacements jump in proportion to the tractions, for finite volume fraction of reinforcements. The fibers are all parallel, isotropically distributed on the transverse plane, and of circular cross section. Elastic properties of both matrix and reinforcement can be arbitrary, but those of their interfacial bonding are restricted to a particular form of common use. Proposals rely on the combined use of the Hashin–Shtrikman approximation for perfectly bonded systems and the equivalent inclusion concept adapted to the peculiar geometry of fibers. Three distinct approximations are considered which differ in the way the elastic properties of the interfacial bonding are averaged over the interfacial surface; they either involve an arithmetic, a harmonic, or a mixed average. Their accuracy is assessed by confronting them to full-field simulations generated with a Fast Fourier Transform-based algorithm suitably implemented to handle interfacial imperfections. Comparisons for transversely isotropic materials with monodisperse reinforcements confirm the superiority of the harmonic and mixed approximations over the more common arithmetic approximation. Overall, the mixed approximation is found to provide the most accurate estimates for a wide range of interfacial bondings and reinforcement contents. The approximations should therefore constitute a valuable ingredient in mean-field descriptions for fiber-reinforced materials incorporating interfacial deformation processes.