An apparatus includes a flexible container, a port, and a support structure. The container includes a first layer coupled to a second layer to define a storage volume within which a tissue specimen can be contained. The first layer is characterized by a first stiffness and the second layer characterized by a second stiffness. An edge of the first layer is spaced apart from an edge of the second layer to define an opening into the storage volume. The edge of the first layer and the edge of the second layer are configured to form a peelable seal that hermetically seals the storage volume such that the first layer can be peeled away from the second layer to expose the storage volume. The port is coupled to the flexible container and allows fluid communication between the storage volume and an external volume. The support structure is configured to support the tissue specimen within the storage volume and is characterized by a third stiffness. The third stiffness is greater than the first stiffness and the second stiffness.