Recently stress analysis of a notched or cracked body has been developed by the finite element method. For this purpose, however, we have to use extremely fine meshes in the vicinity of notch corners or crack tips, and it causes a great deal of work in preparation of in-put data. The senior author suggested an effective technique called the method of superposition of analytical and finite-element solutions, which has been applied to two-dimensional problems successfully. The stress has a singularity at the crack front. Though it cannot be expressed exactly by the conventional finite-element solutions, the analytical expression for it can be obtained near the crack front, and will be used as an auxiliary solution in this method. The solution in the whole domain is given by the sum of the analytical auxiliary solution and a residual regular one which can be obtained accurately by the conventional finite element method. The singularity in the expression for the stress and accordingly the stress intensity factor can be determined from the analytical part of the solution. In this paper the authors have attempted to develop this method for axisymmetric problems. As numerical examples, the stress intensity factors for a round bar with a penny-shaped or circumferential crack have been obtained. The numerical results calculated herein show a good agreement with those obtained by the previous authors analytically. In the case of a shallow circumferential crack, there is a difficulty to determine a proper three-dimensional auxiliary analytical solution. It has been overcome by adapting the two-dimensional solution near a crack.