In simulations of eddy current inspections using the boundary element method (BEM) is is often the case that the calculation of the system matrix carries the largest computational cost. This matrix calculation typically makes use of a Green's function expressed as a Fourier integral. The present study has aimed to reduce the computational cost by adopting an alternative approach for the rapid computation of the Green's function in the spatial domain. This is possible by employing Sommerfeld integral expressions and by approximating them in terms of discrete complex images. Theoretical results are compared to both benchmark experimental data for a semi-elliptical crack and to numerical data from a finite element commercial package. Agreement is excellent over a wide frequency range.