A device for gripping a flexible container, such as a bag filled with fluid, comprising a chamber that is open on one side with a peripheral wall that encloses the open side, a container support that extends in the peripheral direction inside the peripheral wall, as well as an orifice for connecting a vacuum source to the chamber, wherein the chamber can be placed with the open side against the container, such that a vacuum can be generated between the chamber and the container for bringing the container in to contact around the container support transversely to the peripheral direction. The orifice is outside the container support and extends in the peripheral direction.