A novel methodology is presented for the efficient reliability analysis of plate structures containing cracks with the Dual Boundary Element Method (DBEM). The derivatives of the DBEM plate formulations for the Crack Surface Displacement Extrapolation (CSDE) method have been derived for the first time and are used as part of an Implicit Differentiation Method (IDM) for the efficient calculation of Stress Intensity Factor (SIF) sensitivities. A numerical example is investigated in which results from the presented CSDE methodology are compared to those from the J-integral. The SIF sensitivities were used with the First-Order Reliability Method (FORM) to determine the reliability of a plate structure containing a crack. Results indicate that the proposed CSDE methodology is capable of providing estimates for reliability that are very similar to those provided by the J-integral. Given that the proposed CSDE methodology can be easier to implement, it could prove to be an effective alternative to the J-integral for the efficient reliability analysis of plate structures containing cracks.