The variation of stress intensity factors along the crack front of a crack penetrating through the thickness of a plate is analysed by the finite-element method on the basis of concept of the superposition of analytic and finite-element solutions, which has been successfully employed for two-dimensional and axi-symmetric three-dimensional crack problems. In three-dimensional problems, difficulties exist in finding analytic solutions of the governing differential equations, which have the singularity for cracks. In the present paper the authors propose a method of constructing appropriate series of analytic solution which does not satisfy the governing equation but can easily approximate the variation of stress intensity factors. As a numerical example the stress intensity factor of a compact tension specimen is calculated. It is shown that the stress intensity factor takes the maximum on the middle-surface, which is 7-15% higher than the two-dimensional value.