Cryopreservation via vitrification (glass formation) is a promising approach for long-term preservation of large-size tissues and organs. Unfortunately, thermomechanical stress, which is driven by the tendency of materials to change size with temperature, may lead to structural failure. This study focuses on analysis of thermomechanical stress in a realistic, pillow-like shape cryobag as it is cooled to cryogenic storage, subject to sufficiently high cooling rates to facilitate vitrification. Contrary to common perception, it is demonstrated in this study that the maximum stress in the specimen does not necessarily increase with increasing size of the specimen. In fact, the maximum stress is affected by the combination of two competing effects, associated with the extent of the temperature gradients within the specimen and its overall volume. On one hand, the increase in specimen size gives rise to more prominent temperature gradients, which can intensify the thermomechanical stress. On the other hand, the temperature distribution at the core of larger specimens is more uniform, which leads to a larger portion of the specimen transitioning from fluid to a glassy material almost instantaneously, which carries a moderating effect on the overall mechanical stress at the glassy state (i.e., lower residual stress). In conclusion, this study demonstrates the role of container shape optimization in reducing the thermomechanical stress during cooling.