Ball grid array solder joint reliability is known to be dependent on the shape of solder joints after reflow. To ensure good solder joint formation and prevent solder bridging, it is critical to understand the amount of paste volume needed during assembly and reflow. The final shape of the solder joint is a function of surface tension, wetting area, gravity, and applied forces. In this paper, a new methodology to simulate solder joint shape is presented. Large deformation viscoplastic finite element analysis is used to simulate incompressible fluid flow. A numerical model for surface tension is outlined and validated with closed-form solutions. The results of the numerical model are compared to other known solder joint shape prediction methods. The effects of package weight, coplanarity, warpage, paste volume, pad misregistration, and joint construction on solder joint shape are then analyzed. Recommendations are provided on ways to maximize standoff height and avoid bridging. Finally, the formation of leadless solder joints is studied and compared to experimental data.