We have developed a microstructure sensitive fracture model for single crystal tungsten to predict its fracture behavior at the microscale. As tungsten is proposed to be the plasma facing armor component of fusion reactors, understanding its failure mechanisms is critical for safe operation. We used a crystal plasticity-based finite element model coupled with the extended finite element method (X-FEM) to account for the anisotropy of fracture planes in BCC tungsten. In X-FEM discontinuous enrichment functions are added to the finite element formulation to model discontinuities in the solution which are mesh independent. Using X-FEM we are able to simulate crack propagation in any direction, without specifying the crack path ahead of time. Additionally, X-FEM saves computational time as re-meshing around the crack is not required. We compared the performance of X-FEM to cohesive zone elements and investigated the effectiveness of different fracture propagation criteria which take into account the microstructure and preferred crack systems of tungsten. The simulation findings are compared with data from single crystal microcantilever experiments.