The study of bi-material notches is becoming a topical problem as they can model geometrical or material discontinuities efficiently. Assessing the conditions for crack initiation in bimaterial notches makes it necessary to calculate the generalized stress intensity factors H. In contrast to the determination of the K factor for a crack in an isotropic homogeneous medium, for the ascertainment of a generalized stress intensity factor (GSIF) there is no procedure incorporated in the calculation systems. The calculation of these fracture mechanics parameters is not trivial and requires certain experience. Nevertheless, the accuracy of the H-factor calculation directly influences the reliability of the assessment of the singular stress concentrators. Direct methods of the estimation of H factors usually require choosing the length parameter entering into the calculation. Two types of direct methods of calculating the GSIFs are presented, tested and mutually compared. Recommendations for reliable estimation of H factors are suggested.