The method of superposition of analytical and finite-element solutions is proposed for determining three-dimensional distributions of the stress intensity factor; the singular part of the solution is expressed by a linear combination of analytical solutions, and the rest by a finite-element solution. The method is applied to a round bar with a circumferential crack and plates with penetrating cracks. Detailed distributions of the stress intensity factor near the plate surfaces are investigated with the aid of Benthem's theory, which shows that less than 0.5% of the plate thickness is severely influenced by the plate surfaces in the case of a compact tension specimen. Computations for the present method can be performed with a general purpose program for finite element analysis without using special elements.