<p>Resolving the different failure modes of material domains under combined load states plays a crucial role in designing against catastrophic failure. Within elastic fracture mechanics, the Scaled Boundary Finite Element Method has attracted attention for its ability to solve problems in unbounded domains or singular fields, such as crack tips. However, inherent material heterogeneities or imperfections at the micro- or mesoscale considerably affect their fracture toughness. To account for such cases, uncertainty quantification emerges as an appealing methodology. In this work, a stochastic scaled-boundary finite element method is developed to quantify the variability in crack paths arising from variations in underlying material properties within an elastic fracture mechanics setting. To this end, the Karhunen-Loève expansion is employed to discretise the random fields, and uncertainty is propagated to the evaluation of the Stress Intensity Factors and eventually the simulation of crack propagation. Crack propagation is simulated via an adaptive mesh refinement strategy leveraging the advantages of quadtree decompositions and polygon clipping. The merits of the proposed approach with respect to accuracy and efficiency are examined through a set of benchmarks.</p>