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In the present contribution the joint of orthotropic materials is modelled as an orthotropic bi-material notch. The singular stress field near the notch tip is investigated. Depending on the notch geometry and materials, the stress singularity exponents are determined. A criterion for the direction of crack nucleation is formulated based on angular dependences of the mean value of tangential stress in the notch tip vicinity. For various combinations of the orthotropic parts of the bi-material notch the crack initiation direction was investigated by means of the finite element method as well as on the basis of the analytical-numerical approach described in the paper. Results of both methods are mutually compared and discussed.