This paper describes the numerical prediction of the thermal fatigue life of a $mu$BGA(Micro Ball Grid Array) solder joint. Finite element analysis(FEA) was employed to simulate thermal cycling loading for solder joint reliability. 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. The results show that Sn-3.5mass%Ag solder had the longest thermal fatigue life in low cycle fatigue. Also a practical correlation for the prediction of the thermal fatigue life was suggested by using the dimensionless variable ${gamma}$, which was possible to use several lead free solder alloys for prediction of thermal fatigue life. Furthermore, when the contact angle of the ball and chip has 50 degrees, solder joint has longest fatigue life.