It has been well known that ductile fracture of steel is accelerated by triaxiality stresses. The characteristics of ductile crack initiation in steels are evaluate quantitatively using two-parameter criterion based on equivalent plastic strain and stress triaxiality. Recently, the characteristics of critical crack initiation of steels are quantitatively estimated using the two-parameter, 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 critical condition to initiate ductile crack using two-parameter. Then, the crack initiation testing were conducted under static and dynamic loading. To evaluate the stress/strain state in the specimens especially under dynamic loading, thermal elastic-plastic dynamic FE-analysis considering the temperature rise was used. The result showed that the critical global strain to initiate ductile fracture in specimens with strength mismatch under various loading rate cu be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mismatch and dynamic loading effects on stress/strain behavior.