In this paper, an analytical form for the Jones matrix of a real spun fiber has been obtained, taking into account a slight deviation of its properties from an idealized representation of this fiber by the rotation matrix. The derivation was made within the framework of the optical element model with phase anisotropy. The features of using the Jones matrix of a real spun fiber in analysis of practical fiber-optic circuits and modeling their signals were considered. The experiments with the spun fiber revealing the parameter deviations of the polarization modes of the real spun fiber from the idealized model and allowing estimation of this deviation level were performed.