In flip-chip solder joints, Cu has been used as a under-bump metallization (UBM) for its excellent wettability with solders. In addition, electromigration has become an crucial reliability concerns for fine-pitch flip chip solder joints. In this paper, 3-D finite element method was employed to simulate the current density distribution for the eutectic SnPb solder joints with 5 mu m, 10 mu m, and 20 mu m thick Cu UBM. It was found that the thicker the UBM is, the lower the maximum current density inside the solder. The maximum current density decreased from 4.37 X. 10(4) A/cm(2) to 7.54 x 10(3) A/cm(2) when the thickness of the UBM changed from 5 gm to 20 mu m. Thicker Cu UBM can, effectively relieve the current crowding effect inside the solder.