An interchangeable container for a system for building a mold body by forming superimposed layers of granular material, the granular material locally and selectively hardened layer by layer. The container includes a bottom structure that is displaceable in the interior of the container in a direction in parallel with the container side walls and at least one spindle drive having a vertical screw spindle rotatably mounted in a container side of the container, and a spindle screw nut on which the bottom structure is supported. The bottom structure can be lowered step by step in the interior of the container by the spindle drive.