Microcracking is often observed in the resin pockets of as-cured 3D woven composites with significant through-the-thickness fiber constraint. The resin is subjected to a triaxial tensile stress during cooling due to thermal expansion mismatch and shrinkage during curing. However, the temperature dependence of the failure surface for resins subjected to triaxial tensile stress is not known and there is no standard measurement method for applying a triaxial tensile stress. We have developed a novel method for measuring the triaxial tensile failure stress surface by confining the shrinkage of the resin to tubes of different thicknesses and made of materials with different thermal expansion coefficient. The difference in thermal contraction and shrinkage between the resin and the confining tube subjects the resin to a triaxial tensile stress during cooling and curing. We vary the stress-temperature state by selecting tubes with different coefficient of thermal expansion. We infer the stress in the resin from the deflections of the tube measured by a high resolution dilatometer assuming that the tube is a linear elastic, thick-walled pressure vessel.