It has been well known that the ductile cracking of steel would be accelerated by triaxial stress state. Recently, the characteristics of critical crack initiation of steels are quantitatively estimated using the two-parameters, that is, equivalent plastic strain and stress triaxiality, criterion. This study is paid to the fundamental clarification of the effect of geometrical heterogeneity and strength mismatching, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on ductile crack initiation behavior. Also, the ductile crack initiation testing were conducted under static and dynamic loading using round bar specimens with circumferential notch and strength mis-matching. The result showed that the nominal strain at ductile crack initiation of circumferential notch specimens small then the round bar specimens for effect of geometrical discontinuity. Also, the nominal strain at ductile crack initiation was decreased with decrease of notch root radius of curvature.