The fictitious notch rounding concept is applied for the first time to V-notches subjected to combined modes I and III loading. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been employed in the present contribution. An analytical method based on the original Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode mixity ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. The determined support factors are validated by means of a purely numerical basis by means of a large bulk of FE models. Finally the criterion is applied to a set of data taken from the literature.