Three-dimensional simulations for relieving the current crowding effect in solder joints under current stressing were carried out using the finite element method. Three possible approaches were examined in this study, including varying the size of the passivation opening, increasing the thickness of Cu underbump metallization (UBM), and adopting or inserting a thin highly resistive UBM layer. It was found that the current crowding effect in the solder bump could be successfully relieved with the thick Cu UBM or with the highly resistive UBM. Compared to the solder joint with Al/Ni(V)/Cu UBM, for instance, the maximum current density in a solder bump decreased dramatically by a factor of fifteen, say from 1.11 × 105 A/cm2 to 7.54 × 103 A/cm2 when a 20-μm-thick Cu UBM was used. It could be lowered by a factor of seven, say to 1.55 × 104 A/cm2, when a 0.7-μm UBM of 14770 μΩ cm was adopted. It is worth noting that although a resistive UBM layer was used, the penalty on overall resistance increase was negligible because the total resistance was dominated by the Al trace instead of the solder bump. Thermal simulation showed that the average temperature increase due to Joule heating effect was only 2.8 °C when the solder joints with UBM of 14770 μΩ cm were applied by 0.2 A.