A tissue penetrating instrument used in the medical field which may or may not be embodied in the form of an obturator associated with a trocar assembly, wherein the instrument includes an elongated shaft having a penetrating tip mounted on one end. The penetrating tip includes a base secured to the one end of the shaft and a distal extremity spaced longitudinally outward from the base and formed into an apex which may be defined by a point or other configuration specifically structured to facilitate penetration or puncturing of bodily tissue. The penetrating tip further includes an exterior surface extending continuously between the apex and the base and configured to facilitate puncturing of the tissue and an enlargement of an access opening formed in the tissue, in a manner which facilitates separation of the tissue and minimizes cutting, severing or otherwise damaging the contiguous bodily tissue surrounding the access opening.