A support device (20), mounted on an upper edge of a container (3), includes lifting elements that define a support surface (22) which extends transversely outwards from an inner edge (55). The upper end (2b) of a flexible pouch for biopharmaceutical product can rest on this support surface, the rest of the 3D-type pouch extending into the container. The slot (23) which separates the support surface into two portions defines a guide path for a flexible supply line (9a, 9b) for the pouch (2) that is connected at its bottom to the end (2b). A convex surface is formed at the rear end of the slot and above the edge of the container, so as to guide and facilitate the passage of the line (9a) into the housing, when the filling state is sufficiently advanced. The causes of poor deployment of the pouch are thus minimized, without human intervention.
