The invention is directed towards a bladeless obturator (18) for wedging through muscle fiber layers (41,43,45) to safely cut through to the abdominal cavity (32) in order to apply a cannula (12). The invention comprises a bladeless obturator (18) having a tip (27) with side sections (50,52) whose distal portions are twisted with respect to their proximal portions and with an intermediate section (54,56) separating the side sections, wherein the distal portion of the intermediate section is twisted in a first direction and the proximal portion is rotated in a second direction opposite to the first direction.