In the article, stress intensity factors for a straight crack of a mixed-fracture mode in the orthotropic material and in its particular case, namely, in the material with cubic symmetry, have been calculated. The displacement and stress extrapolation method based on the Lekhnitskii formalism was used. For considered classes of materials, the explicit expressions for influence matrix elements were obtained through the elastic constants of the material in the cases of its planar-stressed state and given a non-zero angle between the material’s anisotropy and the crack's axes. Influence matrix properties were analyzed systematically. The obtained results of verification of considered variants of the displacement and stress extrapolation method exhibited a good agreement between the numerical and analytical solutions (the difference did not exceed 0.8 %).