Compositions and methods for the shipping, packaging, and freezing of whole or partial biological materials including but not limited to cells, tissues, and organs, designed to simultaneously reduce freezing damage and maintain tissue structure. This is achieved using a composition for transport and ambient or cold storage, a cryopreservative suitable to reduce damage during the cooling process, and a device for supporting the biological material during the freezing process. Each of the transport media, cryopreservative, and device to support freezing are compatible for use in a shipping and processing chain of events but are not intended to be limiting for use only with each other. These aspects of the present invention are applicable to transport and preservation of biological materials including but not limited to amniotic membrane of the placenta and umbilical cord but are applicable to preservation of cellular and acellular biological materials generally.