The present paper summarizes the results of some numerical calculations carried out on the basis of a recent wide experimental research. The calculations are performed on axisymmetric specimens weakened by V notches consisting of a large bulk of different shapes. The specimens are subjected to multiaxial fracture loading (tension + torsion). Stress and strain fields in the whole specimens are evaluated herein by using the finite element method (FEM). Special attention is paid to the changing distribution of stresses induced by loading and notch shape. By taking advantage of the numerical calculations carried out in the present investigation, a new non-local fracture criterion for notched specimens under multiaxial loading is proposed and successfully employed and compared with some data taken from the recent literature. (C) 2017 Published by Elsevier Ltd.