It has been well known that ductile fractures of steels are accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using two-parameter criterion based on equivalent plastic strain and stress triaxiality. It has been demonstrated by authors using round-bar specimens with circumferential notch in single tension that the critical strain to initiate ductile crack from specimen center depends considerably on stress triaxiality, but surface cracking of notch root is in accordance with constant strain condition. This study fundamentally clarifies the effect of strength mismatch, which can elevate plastic constraint due to heterogeneous plastic straining under static loading, on critical conditions for ductile cracking from the pre-notch root. In order to evaluate the stress/strain state in the pre-notch root of specimens, a thermal elastic-plastic finite element (FE) analysis has been carried out.