A numerical analysis by means of the ANSYS code was performed in order to identify the ratio of both stress intensity factors and crack tip opening displacements for a cylindrical specimen with circumferential V-notch loaded by remote pure shear stress. This kind of loading produces pure mode II and III loading in four points on the circumferential crack front while the mix mode II+III exists in all other crack front points. In the linear-elastic range, the ratio of maximum values of mode III and mode II stress intensity factors was found to be . On the other hand, the ratio of crack tip opening displacements in the elastoplastic range approaches . These results can be used for the construction of fatigue crack growth rate curves in austenitic and ferritic steels measured in the near-threshold and near-fracture regions by means of a special testing device.