Stress intensity factor (SIF) is the foundation and key of predicting the residual strength and fatigue crack growth for structures with multiple site damage (MSD). Considering the contaction and friction, three-dimensional finite element models of lap joints with MSD are established. The distribution and variation of SIFs at each crack tip with different crack lengths, rivet types and damage modes are investigated. Results show that K_I is dominant, while K_II and K_III are negligible. Due to the secondary bending, rivet deformation and plate thickness, the SIF reaches minimum at outside surface, and the faying surface side is larger, while the maximum is located in the plate for almost all crack length. The SIFs values increase substantially due to the interaction of MSD cracks. The shorter the distance between cracks, the stronger the interaction. When the crack length is the same, the integral average value of SIFs along the crack front for the countersunk rivet is larger than that of the flat head rivet. The SIF value at the faying surface of countersunk rivet is larger than that of the flat head rivet, while the trend of SIF at the outside surface is opposite.