In this paper, a new method was proposed for evaluating the high-cycles fatigue strength of BGA (Ball Grid Array) packages with Pb-free solder and Pb solder due to a vibration. Attaching a weight induced mixed mode stress (more than sigma(n)/tau(n) = 1 where sigma(n) and tau(n) are the maximum normal and shear stresses, respectively) in the solder ball of a package. (Actually, a mixed mode stress (sigma(n) /tau(n) = 1) occurs in no-weight case) To consider the effect of a stress ratio, the four kinds of weights (sigma(n)/tau(n) = 2, 4, 5, and 6) were prepared. In general way, the frequency of a test influences the fatigue strength of a package due to a low melting point of solder. However, the frequency didn't affect it, within a range (15-25Hz) used in this study. To confirm whether the solder ball of a Pb-free and a Pb behaves elastically or not within the range of 10similar to25Hz, a FEM analysis was performed with Two-step full and sub-modeling. Both results coincide with each other well. The test data of the vibration fatigue for Pb-free and Pb packages were classified by the nominal shear stress and an Effective Von Mises stress which was calculated by FEM. Although the result classified by the effective Von Mises stress shows the different estimation of a. vibration fatigue life of Pb-free packages according to a stress ratio (sigma(n)/tau(n)), the result classified by the nominal shear stress shows that each vibration fatigue life can be fitted to a, line without the effect of stress ratio (sigma(n)/tau(n)). From a cross-section cutting method and EDX microprobe analysis, the failure mechanism was analyzed. To observe a cross-section of package, the packages of Pb-free and Pb were cut and polished before a fatigue test. During a fatigue test, the cross-section was observed successively by An optical microscope. Though an intermetallic compound region in both of packages and a Pb rich region in a Pb package were confirmed by EDX microprobe analysis, a vibration fatigue induced a crack in a solder ball itself where a stress concentration was occurred under mixed mode stress condition. The position of stress concentration. in FEM analysis coincides with the cross-section of a failure package.