Summary: This paper deals with the generalization of \(T\)-integral to crack growth process in viscoelastic materials. In order to implement this expression in a finite element software, a modelling form of this integral, called \(A\theta\), is developed. The analytical formulation is based on conservative law, independent path integral, and a combination of real, virtual displacement fields, and real, virtual thermal fields introducing, in the same time, a bilinear form of free energy density \(F\). According to the generalization of Noether’s method, the application of Gauss Ostrogradski’s theorem combined with curvilinear cracked contour, \(T_v\) is obtained. By introducing a volume domain around crack tip, the modelling expression \(A\theta\) is also defined. Finally, the viscoelastic generalization through a thermodynamic approach, called \(A_v\), is introduced by using a discretisation of the creep tensor according to a generalized Kelvin Voigt representation.