This study is focussed on the numerical prediction of the thermal fatigue life of a ${mu}BGA$(Micro Ball Grid Array) solder joint. Numerical method is used to perform three-dimensional finite element analysis for Sn-37mass%Pb. Sn-3.5mass%Ag solder alloys during the given thermal cycling. Strain values, along with the result of mechanical fatigue tests for solder alloys were then used to predict the solder joint fatigue life using the Coffin-Manson equation. In this study, a practical correlation for the prediction of the thermal fatigue life is suggested by using the dimensionless variable $gamma$. As a result. it could be found that Sn-3.5mass%Ag has longer fatigue life than Sn-37mass%Pb in low cycle fatigue. In addition. the result with ${gamm}ashow$a good agreement with the FEA results.