Abstract: The 3D finite element analysis model of plastic ball grid array(PBGA) stacked lead-free solder joints with underfills was developed. By using ANSYS the finite element analysis was performed based on the model with random vibration. The influences of PBGA assembly structure, solder joint material, underfill elastic modulus and underfill density on PBGA stacked lead-free solder joint stress and strain under random vibration load were respectively studied. The results show that comparing to the no-underfill stacked solder joints the stress and strain in the stacked solder joint can be effectively reduced under random vibration load. When other conditions being equal, for Sn95.5Ag3.8Cu0.7, Sn96.5Ag3Cu0.5, Sn-3.5Ag and Sn63Pb37, the lead free Sn-3.5Ag stack solder joint has the minimum stress and strain while the lead-free SAC305 stack solder joint has the maximum stress and strain in the solder ball. The stress and strain in the lead-free stacked solder was reduced with the increase of underfill elasticity modulus. With the increase of the underfill density, the stress and strain in the stacked lead-free solder joint increased correspondingly.