A boundary element method (BEM) for the analysis of the semipermeable crack is developed using the numerical Green’s function approach. The extended crack opening displacement (COD) of a straight crack is represented by the continuous distribution of extended dislocation dipoles, with the built-in √r COD behavior, which is integrated analytically to give the whole crack singular element (WCSE) equipped with the √r COD and the 1/√r crack tip extended stress singularity. Linear BEM solvers for the impermeable and permeable cracks are developed first and then an iterative procedure to reach the semipermeable solution using the impermeable and permeable solvers is proposed. The convergence study is performed for the single cracks in the infinite and finite bodies with associated numerical results for the extended stress intensity factors (SIFs) and other variables. The proposed numerical Green’s function approach does not require the post-processing for the accurate determination of the extended stress intensity factors and is ideally suited for the proposed nonlinear iteration scheme for the semipermeable cracks.