Triaxial residual tensile stresses resulting after cooling a 3D woven composite from the curing temperature cause cracking in the resin pockets for weave architectures that have high through‐the‐thickness constraint. We show how curing cycle modifications can reduce the hydrostatic tensile stress generated by thermal mismatch during cooling of Hexcel RTM6 epoxy resin constrained in a quartz tube which simulates extreme constraint in a composite. The modified curing schedule consists of a high temperature cure to just before the glass transition, a lower temperature hold that takes the resin through the glass transition thereby freezing in the zero stress state, followed by high temperature cure to bring the resin to full conversion. We show that this process is sensitive to heating rates and can reduce the zero stress state of non‐toughened RTM6 resin to a temperature similar to a commercial rubber‐toughened resin, Cycom PR520. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43373.