Cryopreservation via vitrification is a promising means for long-term preservation of large-size specimen (vitreous means glassy in Latin). Vitrification involves relatively fast cooling and rewarming rates, potentially giving rise to thermomechanical stress driven by differential thermal expansion in the cryopreserved specimen. Thermomechanical stress is one of the major causes of cryopreservation failure, resulting in structural damage such as fractures and plastic deformation. The general objective of this dissertation is to analyze the resulting thermomechanical stress during vitrification and to propose means to alleviate it, while the presentation of the work is focused on five topics relating to the different stages of cryopreservation process. A typical vitrification protocol begins with cooling the specimen to storage temperature, followed by indefinite storage below glass transition temperature, and finally rewarming it from storage to room temperature. By contrast, the topics presented follow the reverse order in the order of significance, starting with thermomechanical stress analysis during the rewarming phase of the vitrification protocol (Chaps. 2 & 3), where the onset of rewarming has been identified as most susceptible to structural damage. For that purpose, volumetric rewarming techniques like nanowarming and direct electromagnetic heating have been demonstrated most effective. Consistently, the presentation of the first topic (Chap. 2) includes a numerical framework for thermomechanical stress calculations relating to specimen recovery from cryogenic storage by means of electromagnetic heating in the radiofrequency (RF) range. A pillow-like cryobag shape is the base geometric model of the second topic of investigation (Chap. 3), while proposing various strategies to reduce thermomechanical stress during rewarming, including nanowarming. Unfortunately, the specimen cannot be exposed to a conceptually similar volumetric effect of cooling, where the third topic of investigation concerns thermomechanical stress development during that stage of cryoprotocol (Chap. 4). It is demonstrated there 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. The importance of thermomechanical material properties for accurate modelling has been repeatedly discussed in this dissertation, where measurements of the thermal expansion coefficient takes center stage as the fourth topic of this dissertation (Chap. 5). This study includes investigation of the thermal expansion behavior of commonly used cryoprotective agents (CPAs) and compilation of their densities. The final topic of investigation in this dissertation is polarized-light cryomacroscopy, including validation of previously developed numerical methods for estimation of thermomechanical stress (Chap. 6). Also included there is a three-step numerical framework to calculate effects of photoelasticity. The accumulated knowledge underlying this dissertation can serve as the basis for optimization of the cryopreservation protocols, with the goal of reducing thermomechanical stress and preserving structural integrity.