Key to the success of natural and engineered tissues becoming clinically available until needed is their long-term storage at low temperatures. This can be implemented by means of freezing or vitrification. To this end, vitrification offers an attractive approach for tissue banking by forming an amorphous glass both intra- and extracellularly and thereby avoiding the harmful effects of ice formation. Generally, high concentrations of cryoprotectants (CPAs) are used in conjunction with high cooling and warming rates to achieve this. However, hurdles associated with applying this technique include the ability to adequately deliver and remove CPAs due to cellular osmotic and cytotoxic effects as well as achieving adequate cooling and warming rates throughout the tissue to avoid ice formation. The aim of this work was to account for these factors in designing cryopreservation protocols for native and engineered tissues that had intrinsically different characteristics, including tissue size and extracellular matrix properties. The tissues investigated were two types of three-dimensional, cell encapsulated systems consisting of murine insulinomas and murine embryonic stem cells, and native articular cartilage. A mathematical 3-D CPA transport model was developed to predict cell volume excursions and intracellular CPA equilibration and applied to cryopreserve an engineered tissue. This thesis established a systematic methodology to design cryopreservation protocols using experimental measurements and mathematical model for tissues.