A unified general treatment of the propagation of longitudinal waves in coaxial anisotropic assembly of fiber systems is presented. The fiber system consists of an arbitrary number of coaxial layers, each possessing transversely isotropic symmetry properties, that are either perfectly attached at their interfaces or bonded via imperfect interface zones. The single fiber system is either embedded in an infinitely extended solid or fluid host or kept free. As a natural extension of the single fiber case, uniformly distributed fiber systems in a matrix material, which model unidirectional fiber‐reinforced composites, are also studied. All solutions are derived in the form of dispersion relations using the transfer matrix technique. Imperfect interface zones are modeled by degenerate transfer matrices reflecting jumps in the field variables of the neighboring layers. The results are numerically illustrated for a wide range of applications.