Three-dimensional simulations on current-density distribution in solder joints under electric current stressing were carried out by finite element method. Five underbump metallization (UBM) structures were simulated, including Ti/Cr–Cu/Cu thin-film UBM, Al/Ni(V)/Cu thin-film UBM, Cu thick-film UBM, Ni thick-film UBM, and Cu/Ni thick-film UBM. The maximum current density inside the solder occurs in the vicinity of the entrance of the Al trace into the solder joint, while there is no obvious current crowding effect in the substrate side of the joint. The crowding ratio, which is defined as the maximum current density inside the solder divided by the average value in the UBM opening, is as high as 24.7 for the solder with the Ti/Cr–Cu/Cu UBM. However, it decreases to 23.4, 13.5, 8.7, and 7.2 for the rest of the UBM structures, respectively. Solder joints with thick UBMs were found to have a better ability to relieve the current crowding effect. The simulation results are in reasonable agreement with limited published data. The solder joints with higher current crowding ratios have a shorter electromigration failure time.