C/SiC (carbon fiber-reinforced silicon carbide) composites are widely used in the aerospace industry and for the fabrication of high-temperature parts owing to their excellent heat and chemical resistances. In this study, the tensile properties of C/SiC composite tubes manufactured by a filament winding method were examined via hoop tensile testing, and the optimal testing conditions were determined by comparing them with the properties of a composite plate specimen. It was found that during tensile testing, bending stress was generated and the strain inside and outside of the gauge section of the composite specimen is shown as tensile and compressive, respectively; as a result, premature damage occurred, which was not observed for the plate specimen. In order to minimize this effect, tensile testing was performed under the improved conditions, at which the side of fixture was close to the side of the test specimen, and the distance between the upper and lower fixtures was small. However, the relatively low strain to failure (which is a unique characteristic of C/SiC composites) suppressed the induction of both strain inside and outside the specimen in the tensile direction, which led to lower tensile strengths of the composite tubes as compared to that of the plate specimen. Because the tensile modulus calculated in this study is very close to that of the plate specimen, the hoop tensile testing method is suitable for determining the modulus values of C/SiC composites.