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This work presents a crack propagation analysis using an alternative boundary element method (BEM), in both deterministic and probabilistic approach. The fracture effects are captured using an initial stress field, this procedure leads to the appearance of a variable called dipole and responsible for representing the cohesive zone. Both geometry and fracture boundary are discretized using linear elements, the fracture elements are discontinuous. Regarding the structural reliability analysis, the boundary element formulation was coupled with the reliability algorithms for probabilistic analysis of crack problems. The fracture parameters are treated as random variables. First Order Reliability Method (FORM) is used in order to evaluate the reliability index and the failure probability for fractured problems. A comparative study between the Monte Carlo simulation technique are performed. Numerical examples are presented in order to show the accuracy of the BEM formulation in crack propagation analysis, as well in the assessment of structural reliability in two dimensional problems.