Abstract The extended finite element method (XFEM) is utilized to model the crack propagation in thermo-anisotropic elastic materials. The discontinuity at the crack surface is located and modelled using the level set principle whereas the singularity at the crack tip is handled using special branch enrichment functions derived from the asymptotic analysis following Lekhnitskii׳s formalism in anisotropic media. The crack starts to propagate when the maximum circumferential stress to strength ratio criterion is satisfied. The numerical model is validated by comparing the computed stress intensity factors (SIFs) with the existing ones for static cracks. Eventually, the effect of anisotropy on the crack propagation path is investigated by carrying out several simulations.