Portable electric devices such as mobile phones and portable music players have become compact and improved their performance. High-density packaging technology such as chip size package (CSP) and stacked-CSP is used for improving the performance of devices. CSP has a bonded structure composed of materials with different properties. A mismatch of material properties may cause a stress singularity, which leads to the failure of the bonding part in structures. In the present paper, stress analysis using the boundary element method and an eigenvalue analysis using the finite element method are used for evaluating the intensity of a singularity at a vertex in three-dimensional joints. A three-dimensional boundary element program based on the fundamental solution for two-phase isotropic materials is used for calculating the stress distribution in a three-dimensional joint. Angular function in the singular stress field at the vertex in the three-dimensional joint is calculated using an eigenvector determined from the eigenvalue analysis. The joining strength of interface in several kinds of sillicon-resin specimen with different triangular bonding areas is investigated analytically and experimentally. An experiment for debonding the interface in the joints is firstly carried out. Stress singularity analysis for the three-dimensional joints subjected to an external force for debonding the joints is secondly conducted. Combining results of the experiment and the analysis yields a final stress distribution for evaluating the strength of interface. Finally, a relationship of force for delamination in joints with different bonding areas is derived, and a critical value of the 3D intensity of the singularity is determined.