The purpose of this research is to study the limit failure stresses occurring on the rectangular cross section fiber reinforced curved beam subjected to couple moment at the ends of the geometry. Utilizing analytical methods, closed form solutions are obtained for plane stress conditions. Considering different parameters such as the radial thickness and fiber volume of the beam, stress and displacement fields are investigated in detail. Employing different failure criteria, Tsai-Wu and Norris, calculated failure limit moment and failure location differences in the beam are analyzed. Moreover, various transverse Young’s modulus estimation methods available in the literature, Halpin-Tsai, Rule of Mixture, and Chamis, are considered. Effects of these estimations on the aforementioned fields are carefully handled as well. Using the material properties of glass fiber/epoxy constituents, numerical examples are generated by incorporating semi-analytical effective material property calculation models. Achieved numerical results have revealed that the radial thickness of the beam has more influence than fiber volume in terms of failure moment and stresses. Application of different criteria may cause different failure location acquisitions while mildly changing the limit failure moment. Young's modulus estimation influences the radial displacement prominently. In addition to the acquired results, from a general perspective, this study can be used as a benchmark model for failure stress analysis of related structures and may be expanded with appropriate numerical techniques.