Abstract: A closed-form weight function for radial crack（s） at a circular hole in a finite plate was presented. The weight function was basel on an edge crack surface displacement expression for a polynomial type reference load condition, and therefore the approach is much more general than those in the literature. Analytical stress intensity factor formulae for polynomial and piece-wise-linear crack line stress have been derived, which permit stress intensity factors for arbitrary loadings to be determined with minimal effort. The versatility, cost-effectiveness, easy-to-use and high accuracy of the approach was demonstrated through a practical example of double cracks at a circular hole in a finite plate under biaxial tension.