The study introduces a two-parametric criterion for maximum tangential stresses adapted to the Mode I crack, which includes T-stresses. The difference of this criterion is that the size of the fracture process zone is written with account for the T-stresses, while the tangential stresses in the fracture process zone are equated to the local strength of the material rather than to the ultimate strength, as it is usually done. The paper gives two-parametric fracture criteria for the case of plane stress and strain states, allowing the strain constraint along the crack front. Within the study, we obtained expressions for the effective stress intensity factor which include the T-stresses — ultimate strength ratio, in addition to the stress intensity factor. This expression allows us to determine the most dangerous point of the crack front and, provided we know the fracture toughness of the material, to estimate the crack resistance of the part with the crack. As an example of using the fracture criterion, we considered a semi-elliptical edge crack in a plate stretched in two directions.