This paper deals with a semi-explicit algorithm to reconstruct 2D segment cracks, or 3D planar cracks, in the framework of overspecified boundary data. The algorithm is based on the reciprocity gap concept, introduced by S. Andrieux and A. Ben Abda, which provides explicitely the line (or the plane) support of the cracks. A numerical reconstruction of the cracks, which are actually the support of the solution jump across this plane, is then performed by computing the Fourier expansion of the solution jump itself. After the numerical analysis of the method, some numerical results are presented and commented.