Singular stress occurs at the vertex of interface in three-dimensional joint structures under an external force and a temperature variation. It is very important to estimate the intensity of singularity for evaluating the strength of joints. Until now, the intensity of singularity in the three-dimensional joints is usually obtained by approximating the stress distribution using a power-law equation. In the present paper, a conservative integral proposed by the authors is applied to estimate the intensity of singularity. A suitable radius for integral domain is investigated by varying the size of minimum mesh and the ratio of the radius of integral domain to the width, L₁, of model. It was found that the intensity of singularity was obtained within error of 3% even if the minimum radius of integral domain was equal to the minimum size of element in our conservative integral. The accuracy of calculation reduced with the decrease of the radius of integration domain. The intensity of singularity was obtained within the error of 3% for several values of width in the joint using data of displacements and stresses by the boundary element method. The intensity of singularity could be calculated within error of 3% using an arbitrary radius of integration domain under w/L₁<a/L₁<10^-1 in the range where the radius, a, of integration domain is larger than the minimum size of element and in the singular stress fields.