Mechanical joints such as bolted or riveted joints are widely used in structural components and the reliable determination of the stress intensity factors for corner cracks in mechanical joints is needed to evaluate the safety and fatigue life. This paper analyzes the mixed-mode stress intensity factors of surface and deepest points for quarter elliptical corner cracks in mechanical joints by weight function method and the coefficients included in weight function are determined by finite element analyses for reference loadings. The extended form of the weight function method for two-dimensional mixed-mode to three-dimensional is presented and the number of terms in weight function is determined by comparing the results for the different number of terms. The amount of clearance is an important factor in evaluating the severity of elliptical corner cracks in mechanical joints and even horizontal crack normal to the applied load is under mixed-mode in the case that clearance exists.