Predictive modeling of crack propagation plays a vital role in fracture mechanics. Considering crack propagation in linear elastic materials, the Scaled Boundary Finite Element Method (SBFEM) has demonstrated accuracy in calculating the rate of change of Stress Intensity Factors (SIFs). In particular, (SBFEM) is a powerful tool that provides accurate estimates of the stress field on the crack tip while reducing the dimensionality of the numerical problem by one. Compared to other numerical tools e.g. the FEM, X-FEM, or X-IGA no adjustments to the solution procedure are required and SIFs can be conveniently extracted during post-processing. Inherent imperfections in material properties and initial geometry lead to variations in crack trajectories. By extending these quantities into the random field problem, a stochastic scaled boundary finite element method (SSBFEM) is developed to quantify the crack propagation variability. To this end, this study presents an efficient approach for the estimation of the rate change of SIFs under uncertainty. Furthermore, the formulation of the discretized domain is made using polygons as sub-domains of the SBFEM by considering non-homogeneous material properties in the constitutive equation. Finally, the random fields are created via the Expansion Optimal Estimation (EOLE) and the Karhunen-Loève Expansion (KLE). The research work is implemented in the framework of H.F.R.I call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union –NextGenerationEU (H.F.R.I. Project Number: 15097).