A tissue graft container is provided having an interior space and including a vent which allows fluid (liquid and vapor) to escape from the container during drying of the tissue graft. The vent may be one or more apertures, one or more elongated openings, or a combination thereof, through one or more components of the container. A tissue graft packaging system having a retainer including first and second members with respective first and second pluralities of channels, and configured to removeably interconnect the first and second members in a closed configuration. The first and second pluralities of channels create a continuous interior space. The retainer further includes a vent, such as apertures, slits, etc., through one or both of the first and second retainers, for allowing moisture to escape from the retainer during the drying of a tissue graft contained within the continuous interior space of the retainer.