Abstract: A building construction system for progressively forming a plurality of vertical superimposed concrete segments. A plurality of screw jacks form support columns and carry at their upper ends sub-frames upon which an overlying main frame is positioned. Formworks are suspended from the main frame and are moveable into position for pouring concrete to form the segments. The screw jacks are supported on a horizontal building element preceding a previously constructed horizontal building element and are retractable. The main frame is supported on adjustable struts for repositioning the screw jacks prior to extension to a subsequent segment forming position.