AbstractAn hypersingular integral equation of a three‐dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary‐integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth‐contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd.