In order to optimize the design of unidirectional fiber reinforced composite C-rings, a viscoelastic load relaxation behavior was analyzed under a point load. Initially, the deflection and bending stiffness were calculated based on the elastic beam theory and the viscoelastic relaxation and creep behaviors were derived from the elastic solution using the correspondence theorem. Besides the orthotropic mechanical properties of the composite, asymmetric mechanical property due to the different tensile and compressive properties were also considered. Except the deviation affected by the relatively large thickness of the specimen compared to the radius, the calculated relaxation showed good agreement with the experimental result.