The invention is an improved packaging assembly for storing, distributing, treating, mixing, and dispensing tissue and/or cellular material and/or implantable material. The packaging assembly may include pouches, tubes, and a bag made of a sealable, flexible polymeric material that is open at one end and a needle-free swabable connector attached to the pouch at the other end and acting as a port to allow for the introduction or discharge of biological solutions, rinsing solution, and/or preservation solutions into the packaging assembly. The designed thickness of the wall of the packaging assembly facilitates efficient heat/cold transfer, which is useful for successful controlled rate freezing, quick thawing, and resuscitation of viable cells or tissue. The invention is also useful for combining additional biological fluids with the cellular material or tissue, and for efficient mixing of the biological fluids with the tissue and/or cellular material in the assembly.