An accurate and efficient analytical geometric method is presented for predicting the geometric parameters of the controlled collapse chip connection type solder joint using direct chip attach technology after a reflow process. By this method, the meridian of the solder joint is first discretized as a series of sufficiently fine fragmental arcs. After calculating the internal pressure inside the molten eutectic solder from the forces balance, the meridional and circumferential radii of curvature of each arc are then obtained from the Laplace-Young equation. As a result, the coordinates of each node of the arc and the solder joint geometry can be determined in turn. The factors that affect the final shape of the molten eutectic solder joints, including the solder volumes, external loading, pad size, surface tension of molten eutectic solder, and interfacial surface tension between the molten eutectic solder and the solid high-lead bump are considered herein. The results computed by the analytical geometric method are also compared with those obtained using the Surface Evolver program, the extended Heinrich’s model, and the experimental results. The results of the various approaches are mutually consistent.