Three-dimensional (3D) stacked die packaging has become the trend to improve efficiency for transmitting signals, reduce the volume of the package, and help with functions integration. It is more and more applied popularly in telecommunications. Solder joints, interconnections in the packaging structure, are more easily damaged by critical stress from thermal cycle loading when the component is operating, because the coefficient of the thermal expansion of various materials mismatch. People have studied the common single die during the thermal cycle loading for a long time, but the researches for the stacked die BGA are not as complete. In addition, to protect the environment and comply with legislation, the semiconductor industry wants to find a lead-free material to replace the lead solder joints. Therefore, most extant or new types of packaging started using lead-free material to do thermal cycle testing. The critical solder ball location is not the same as in a single die package where at the die corner, due to it is influenced by stacked die with different geometry, the difference in dice length helps to redistribute the die stress. In this paper, we used FEA software, ANSYS, to build up a 3D thin-profile, fine-pitch, ball grid array (TFBGA) model. The modeling investigated the effect on solder joints under thermal cycle and included deformation, von-Mises stress and strain energy density (SED). Then we utilized Darveaux's approach, which is a common methodology used to calculate the fatigue life based on energy and damage accumulation theories, to predict the fatigue life of the critical solder joint and modify our model with the theory. We changed various kinds of SAC solder joints with different ratios of the components and Anand's constants, analyze the divergence and compared them with the lead solder material. We develop a model to forecast the failure phenomenon and fatigue damage on an electronic package. This would help engineers and designers raise the reliability of the package. In addition, we hope to find a lead-free material that can be substituted for the lead solder material. If this is the case, based on simulating results, we hope to improve it and have much a better reliability performance than the original lead solder.