Abstract The eigensolution of the quasi-orthotropic wedge problem is presented. The degenerate orthotropic material of the wedge is characterized by doubled roots of the characteristic equation. Using the method of singular integral equations, the distribution of the stress field in the quasi-orthotropic plane weakened by semi-infinite rounded V-notch was obtained. The edge of the notch was free of load and the asymptotic stress field defined by a stress intensity factor was set at the infinity. On this basis, the relationship between stress intensity factor at the sharp notch vertex and the normal stress at the vertex of corresponding rounded V-notch with the same opening angle was established. As it was shown in the example, this relationship is asymptotic for finite notched bodies and it can be used to calculate a notch stress intensity factor based on a stress concentration results obtained for a notch rounded with small radius of curvature.