A container evacuation system is provided for viscous flowable materials such as grease, paste or flowable powders. The container system includes a lightweight, rigid exterior, such as a cardboard container. Provided within the container is a flexible containment system constructed of polyethylene sheets or the like. The flexible containment system is provided with a plurality of weldments to create at least two pockets, wherein one pocket contains the flowable material and a second pocket is available to be filled with air, to allow air provided to the second pocket to force the flowable material from the first pocket out through a drain. The system includes a weldment which curves around at least a portion of the drain to crease a funnel which focuses flowable material toward the drain, while reducing the likelihood of a portion of the flexible containment system from obstructing the movement of flowable material out of the first pocket through the drain.