A moisture resistant package for storing and transporting sterile items, such as specimens of human or animal tissue, comprises an inner tray that fits within a moisture resistant outer tray. The inner tray has a cavity for storing the specimen. The specimen is enclosed within the cavity by a non-porous inner lid that is sealed to the inner tray by an adhesive to create a moisture and microbial contaminant resistant environment that prevents moisture uptake into the specimen. The inner tray is enclosed within a complementary shaped cavity of the outer tray by an outer lid sealed to the outer tray to complete the assembly of the package. Thereafter, the package is terminally sterilized (using gas or radiation) so that the inner tray can be introduced into a sterile environment when it is removed from the outer tray. In a preferred embodiment, the inner lid includes at least one through hole to reduce the pressure differential that may occur between the outer tray cavity and the inner tray cavity, which differential may otherwise case premature lifting and separation of the inner lid from the inner tray. In addition, the outer tray and the inner tray may be formed of a sheet of transparent thermoplastic material, such as glycerol modified polyethylene terephthalate so that the specimen can be viewed without opening the package. Preferably, the sheet of material for the inner tray and the outer tray is laminated with a film of moisture barrier material and is deep drawn into a three dimensional die, while substantially maintaining the moisture barrier integrity of the trays.