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 with an axis (77d,77u) which is offset from the axis (23d,23u) of an elongate shaft (21) of the obturator.