A shipping container with an outer shipping container shell and a support assembly for holding a dewar vessel within the outer shipping container shell and providing impact and vibration resistance to the dewar vessel. The dewar vessel has an inner vessel that holds a specimen chamber and plastic foam between its inner wall and the specimen chamber. The specimen chamber allows liquid cryogen to pass through it into the plastic foam, allows liquid cryogen in a vapor phase liquid state to pass from the plastic foam into it, and acts as a filter to prevent particles or fragments of the plastic foam from entering into it. The specimen chamber is an open-celled porous thermoplastic material that is cryogenically compatible such as an aerated polypropylene foam. The plastic foam is an open cell plastic foam such as a phenolic foam. The plastic foam can hold a normal charge of liquid cryogen in a dry vapor state regardless of the container's spatial orientation. The plastic foam can be made of multiple foam segments separated by a capillarity separation layer. A self-venting cap is used to restrict access to the specimen chamber when it forms a compression seal with an inner circumference of the neck of the dewar vessel. The shipping container is configured so that a reservoir will be formed within the dewar vessel when the container rests on its side so that gravity will not force vapor phase liquid cryogen in the reservoir out of the dewar vessel. The shipping container complies with Department of Transportation/International Air Transport Association (DOT/IATA) Dangerous Goods Regulations.