The endurability of solder joints in the ball-grid array (BGA) packaging is crucial to the functioning of the microelectronic system. To improve electronic packaging reliability, this paper is dedicated to numerically optimize solder joint array configuration and study the influence of multi-physical fields on solder joint reliability. The uniqueness of this study is that on the basis of temperature field and stress field, the electric field is added to realize the coupling simulation of three physical fields. In addition, the “Open Angle” is mathematically defined to describe the array configuration, and it was used to reveal the influence factors of solder joint fatigue, including stress, temperature, and current density. In the single solder joint model, the impacts of geometric shape and working conditions on the maximum value and distribution of these evaluation factors (stress, temperature, and current density) were investigated. Overall, the numerical investigation gives the optimal configuration, geometric shape, and working condition of solder joints, which benefits the design of endurable and efficient BGA packaging.