Presented diploma thesis is concerned with problems of a stress singularity exponent and a generalized stress intensity factor determination, by dint the stress field in the vicinity of the stress concentrator can be consecutively determined. This task is possible to sectionalize into three parts. The first part summarizes basic information about linear anisotropic materials, deals with fundamentals of the linear elastic fracture mechanics and introduces its generalization to the case of the generalized stress intensity factors. The second part is dedicated to a special theory of anisotropic elasticity - Lekhnitskii-Eshelby-Stroh formalism (LES). Furthermore, a theory of the psi-integral is introduced, by dint the stress intensity factor is determined. The final part applies the LES theory and the psi-integral to the concrete material configuration of a crack on the bimaterial interface, a special example of a sharp bimaterial notch. By means of analytical-numerical algorithm in ANSYS and Silverforst FNT95 software the stress singularity exponents and generalised stress intensity factors are consecutively computed.