The container includes a lower wall and an erect side wall limiting an upper opening of a housing for accommodating a flexible pouch containing a fluid; containment elements including a containment wall, the gap between its peripheral edge and the side wall being limited; the containment wall adapted to be applied against the pouch and held fixed in this position by holding elements arranged in the container and borne by the containment elements by a structural and functional combination, and being movable between an inactive retracted state and an active expanded state, in which a distal end part is either moved away from the side wall or applied there against without any chance of sliding; and adapted to be applied at any desired location of a zone of the side wall such that the containment wall can be applied and held against the pouch regardless of how full the latter is.