A mold shorter side frame of a continuous casting mold is exchanged integrally as it is to enable on-line change of the thickness of the case piece. As the method, a concave portion for engaging a portion of the moving device and an attaching/detaching mechanism having a fixing jig for fixing the portion of the moving device are disposed at the back of the shorter side frame. Particularly, an attaching/detaching mechanism comprising a concave forming portion having a downwarded opening and a bolt screw passing from the back of the concave forming portion through at least a portion of said portion of the moving device is suitable.