A tissue penetrating medical instrument (10'; 60) structured to be used with a trocar tube, said instrument comprising: a) an obturator comprising an elongated shaft (26'; 62) and including a penetrating tip (22'; 64) disposed at one end of said shaft (26'; 62), b) said penetrating tip (22'; 64) including a base (28'; 66) disposed at said one end and an apex (32'; 72) extending outwardly in spaced relation to said base (28'; 66), c) said penetrating tip (22'; 64) further including an exterior surface (40'; 74) extending between said base (28'; 66) and said apex (32'; 72); the apex (32'; 72) of said penetrating tip (22'; 64) being blunt and said exterior surface (40'; 74) having a cross-section (80, 82) oriented perpendicular to a central longitudinal axis of said shaft (26'; 62) and extending along at least a majority of a length of said penetrating tip (22, 64); and being defined by an elliptical circumferential configuration; the exterior surface (40', 74) comprising a curvilinear configuration extending longitudinally along a majority of its length between the base (28', 66) and the apex (32', 72) and the curvilinear configuration being at least partially defined by a complex curve extending along at least a majority of the length thereof and comprising a curve segment extending outwardly from the apex towards the base; said exterior surface (40'; 74) comprising two surface segments (42', 44'; 76, 78) each extending longitudinally between said apex (32'; 72) and said base (28'; 66), said two surface segments (42', 44'; 76, 78) being at least minimally segregated from one another, characterized in that the curve segment is substantially concave. a) an obturator comprising an elongated shaft (26'; 62) and including a penetrating tip (22'; 64) disposed at one end of said shaft (26'; 62), b) said penetrating tip (22'; 64) including a base (28'; 66) disposed at said one end and an apex (32'; 72) extending outwardly in spaced relation to said base (28'; 66), c) said penetrating tip (22'; 64) further including an exterior surface (40'; 74) extending between said base (28'; 66) and said apex (32'; 72); the apex (32'; 72) of said penetrating tip (22'; 64) being blunt and said exterior surface (40'; 74) having a cross-section (80, 82) oriented perpendicular to a central longitudinal axis of said shaft (26'; 62) and extending along at least a majority of a length of said penetrating tip (22, 64); and being defined by an elliptical circumferential configuration; the exterior surface (40', 74) comprising a curvilinear configuration extending longitudinally along a majority of its length between the base (28', 66) and the apex (32', 72) and the curvilinear configuration being at least partially defined by a complex curve extending along at least a majority of the length thereof and comprising a curve segment extending outwardly from the apex towards the base; said exterior surface (40'; 74) comprising two surface segments (42', 44'; 76, 78) each extending longitudinally between said apex (32'; 72) and said base (28'; 66), said two surface segments (42', 44'; 76, 78) being at least minimally segregated from one another, characterized in that the curve segment is substantially concave.