The two-dimensional problem of advection–dispersion associated with a non-aqueous-phase liquid (NAPL) pool is addressed using the boundary element method. The problem is appropriately posed with an inhomogeneous boundary condition taking into consideration the presence of the pool and the impermeable layer. We derive a Fredholm integral equation of the first kind for the concentration gradient along the pool location and compute the average mass transfer coefficient numerically using the boundary-element method. Numerical results are in agreement with asymptotic analytical solutions obtained for the cases of small and large Péclet number (Pex). The asymptotic solution for small Pex, which is obtained by applying a novel perturbation technique to the integral equation, is used to de-singularize the integral equation. Results predicted by this analysis are in good agreement with experimentally determined overall mass transfer coefficients.