Packaging for prosthetic heart valves including an assembly for stabilizing dry prosthetic tissue implants such as heart valves during storage. The packaging assembly can be used for storing a bioprosthetic heart valve without a liquid preservative solution. The packaging assembly can comprise a holder comprising an engagement structure configured for removably attaching a bioprosthetic heart valve, the holder comprising a shaft. The packaging assembly can also include a storage tray comprising a cavity and an insert sized to provide a cap over the cavity of the storage tray, the insert comprising a slot having a closed central end and an open outer periphery. The shaft of the holder can be non-rotatably retained at the closed central end, wherein the insert defines a flat, generally planar disc comprising at least one of outward projections and flow passages.