In this study, the numerical prediction of the thermal fatigue lie? of a $mu$BGA (Micro Ball Grid Array) solder joint was focused. Numerical method was performed using the three-dimensional finite element analysis for various solder alloys such as Sn-37%Pb, Sn-3.5%Ag, Sn-3.5%Ag-0.7%Cu and Sn-3.5%Ag-3%In-0.5%Bi during a given thermal cycling. Strain values obtained by the result of mechanical fatigue tests for solder alloys, were used to predict the solder joint fatigue life using the Coffin-Manson equation. The numerical results showed that Sn-3.5%Ag with the 50-degree ball shape geometry had the longest thermal fatigue life in low cycle fatigue. A practical correlation for the prediction of the thermal fatigue life was also suggested by using the dimensionless variable γ. Additionally Sn-3.5Ag-0.75Cu and Sn-2.0Ag-0.5Cu-2.0Bi were applied to 6$ imes$8$mu$BGA obtained from the 63Sn-37Pb Solder. This 6$ imes$8$mu$BGA were tested at different aging conditions at 130$^{C}$, 150$^{C}$, 170$^{C}$ for 300, 600 and 900 hours. Thickness of the intermetallic compound layer was measured thor each condition and the activation energy thor their growth was computed. The fracture surfaces were analyzed using SEM (Scanning Electron Microscope) with EDS ( Energy Dispersive Spectroscopy).