A surgical obturator comprising an elongate shaft extending along an axis between a proximal end and a distal end includes a bladeless tip disposed at the distal end of the shaft. The tip has a blunt point and a pair of shorter side surfaces separated by a relatively longer pair of opposing surfaces to form in radial cross-section a geometric shape that has a longer length and relatively narrower width. The side surfaces and opposing surfaces terminate in end surfaces located proximally from the blunt point. The end surfaces extend radially outwardly from opposite locations of the outer surface. A conical surface facilitates initial insertion of the obturator and the geometric shape facilitates separation of consecutive layers of muscle tissue having fibers oriented in different directions and provides proper alignment of the tip between the layers of muscle.