In the classical crack-tip stress field, the singular stresses (r1/2 term) near the crack tip are characterized by a single parameter, i.e. the stress intensity factor K. Therefore, the O(r1/2) term and the secondary non-singular term (T-stress) are always ignored. However, the stress and strain fields around the crack tip are influenced considerably by the T-stress. In this paper, the conventional fracture growth criteria, i.e. the maximum tangential stress criterion is modified to take into account the effect of T-stress, and is used to study the fracture growth when subjected to modes I, II or mixed mode (I/II) loading. The results show that: (1) In the pure mode I loading condition, if the T-stress is negative (compression), the crack growth is stable. However, if the T-stress is positive (tensile), the crack grows along the crack direction only when , otherwise, the crack growth direction will be changed. (2) In the pure mode II loading condition, the crack growth direction and the loading capacity are influenced not only by the stresses along the fracture direction (T-stress) but also by the normal stress on the fracture. (3) For the mixed loading condition, the T-stress consideration in the fracture criteria leads to better agree with the experiments. The positive T-stress results in an increase in crack growth angle, while the negative T-stress decreases that angle. The results reveal that it is benefit to control the T-stress to change the crack growth direction, in order to avoid the most dangerous crack growth direction or stopping/slowing down the overall structural fracture.