The effect of first nonsingular stress term of elastic stress field on fracture toughness around bi-material notch tip is studies in this paper. First, a modified maximum tangential stress criterion (MMTS) is proposed for determination of the fracture toughness at the tip of the interface notches. The proposed criterion takes into account the effect of first nonsingular stress term as well as the singular stress terms. Then, the effect of I-stress on determination of the fracture toughness is studied analytically. Finally, the proposed criterion is applied on a finite element (FE) simulated laboratory specimen. A very good correlation was observed between the FE results and theoretical predictions.