Cryopreservation by vitrification is the only promising solution for long-term organ preservation which can save millions of lives across the world. One of the challenges in cryopreservation of large-size tissues and organs is to prevent fracture formation due to the tendency of the material to contract with temperature. The current study focuses on a pillow-like shape of a cryobag, while exploring various strategies to reduce thermo-mechanical stress during the rewarming phase of the cryopreservation protocol, where maximum stresses are typically found. It is demonstrated in this study that while the level of stress may generally increase with the increasing amount of CPA filled in the cryobag, the ratio between width and length of the cryobag play a significant role. Counterintuitively, the overall maximum stress is not found when the bag is filled to its maximum capacity (when the filled cryobag resembles a sphere). Parametric investigation suggests that reducing the initial rewarming rate between the storage temperature and the glass transition temperature may dramatically decrease the thermo-mechanical stress. Adding a temperature hold during rewarming at the glass transition temperature may reduce the thermo-mechanical stress in some cases, but may have an adverse effect in other cases. Finally, it is demonstrated that careful incorporation of volumetric heating by means on nanoparticles in an alternating magnetic field, or nanowarming, can dramatically reduce the resulting thermo-mechanical stress. These observations display the potential benefit of a thermo-mechanical design of the cryopreservation protocols in order to prevent structural damage.