In this paper, the hypersingular integral equation method (HIEM) is applied to calculate the stress intensity factors of the mixed mode crack problems. The stress fields induced by "two kinds of displacement discontinuity" are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form of (ζ-χ)^-2. In the numerical calculation, two kinds of unknown-functions are approximated by the products of the weight functions and Chebychev polynomials. As examples, the stress intensity factors of the oblique edge crack in the semi-infinite plate are treated. The calculation shows that the HIEM gives rapidly converging numerical results even for extremely oblique edge crack.