A system for shaping a liquid material within a cryostorage bag while undergoing a freezing procedure, said system comprising: a cryostorage bag having a sealed perimeter defining an interior region configured to receive a liquid material, said interior region having an inner perimeter shape; a pair of cushion elements having an outer perimeter and comprising a cut-out shape that is approximately the same shape as the inner perimeter shape of the interior region, said pair of cushion elements being configured to sandwich the cryostorage bag between the pair of cushion elements; a pair of frame elements having an outer perimeter that is approximately the same as the outer perimeter of the pair of cushion elements, and comprising a window having a desired shape, wherein the position of the window approximately corresponds to the interior region of the cryostorage bag when the cryostorage bag and the pair of cushion elements are sandwiched between the pair of frame elements, wherein the cryostorage bag, the pair of cushion elements and the pair of frame elements provide a vessel assembly when the cryostorage bag and the pair of cushion elements are sandwiched between the pair of frame elements; a pair of spacers having an outer perimeter that is approximately the same as the desired shape of the window such that the pair of spacers may be seated within the window of the pair of frame elements with minimal tolerance; and a pair of thermally conductive plates having an outer perimeter that is approximately the same as the outer perimeter of the pair of cushion elements, and comprising a planar inner surface, wherein pair of thermally conductive plates are configured to sandwich the vessel assembly and pair of spacers together during a freezing procedure. a cryostorage bag having a sealed perimeter defining an interior region configured to receive a liquid material, said interior region having an inner perimeter shape; a pair of cushion elements having an outer perimeter and comprising a cut-out shape that is approximately the same shape as the inner perimeter shape of the interior region, said pair of cushion elements being configured to sandwich the cryostorage bag between the pair of cushion elements; a pair of frame elements having an outer perimeter that is approximately the same as the outer perimeter of the pair of cushion elements, and comprising a window having a desired shape, wherein the position of the window approximately corresponds to the interior region of the cryostorage bag when the cryostorage bag and the pair of cushion elements are sandwiched between the pair of frame elements, wherein the cryostorage bag, the pair of cushion elements and the pair of frame elements provide a vessel assembly when the cryostorage bag and the pair of cushion elements are sandwiched between the pair of frame elements; a pair of spacers having an outer perimeter that is approximately the same as the desired shape of the window such that the pair of spacers may be seated within the window of the pair of frame elements with minimal tolerance; and a pair of thermally conductive plates having an outer perimeter that is approximately the same as the outer perimeter of the pair of cushion elements, and comprising a planar inner surface, wherein pair of thermally conductive plates are configured to sandwich the vessel assembly and pair of spacers together during a freezing procedure.