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 rectangular tip (27j) with a conical surface (75j) between two cylindrical surfaces (95j, 99j). At least one ridge (93j) extends radially outwards from the conical surface and from the distal one of the two cylindrical surfaces.