Abstract: A container for storing and transporting semen, e.g., equine semen, along with a corresponding method of packing the container, is provided. The container is formed of an insulated box and an insulated cover. The insulated box and insulated cover each includes a collection of ridges and recesses to create a friction fit between the two that will only work with the insulated cover being placed on the insulated box in a predetermined orientation. A cooling pack is disposed on a floor of the insulated box. An insert is disposed to rest on the cooling pack inside the insulated box, such that the cooling pack is beneath the insert when the insulated box is in an upright position. The insert has at least one chamber for receiving a storage capsule holding the semen sample. The insulated cover frictionally fits on the insulated box and makes contact with the insert to hold the insert in place.