In this paper, the extended Finite Element Method (XFEM) is implemented to compute the Stress Intensity Factors (SIFs) for rectangular media subjected to a hygrothermal loading. In governing hygrothermoelasticity equations, the cross coupled of temperature and moisture fields and temperature-dependent diffusion in some cases are considered. Furthermore, an interaction integral for hygrothermal loading is developed to compute the stress intensity factors. The non uniform mesh of isoparametric eight-nod rectangular element is used in XFEM to decrease the absolute error in SIFs computations. In order to numerical results validation, the SIF of mode I is obtained analytically. The coupled governing equations are firstly decoupled in terms of new variables and then solved by the separation of variable method. According to the results, the moisture concentration gradient has a significant effect on the SIFs so should be considered in the model. Up to reaching temperature to its steady state, the cross coupled of temperature and moisture synchronies their time variation which affects on the time variation of SIF. At early time of thermal shock, the SIF for shorter cracks is not necessarily lesser than the longer ones. Also, the mode I SIF for longer and inclined cracks is smaller. On the other hand, considering the moisture concentration as a temperature function increases the time required to reach the moisture steady state.