Ag3Sn intermetallic growth within Sn-Bi-Ag alloys during relatively slow cooling rates has a pronounced effect on the performance and reliability of solder joints. In this study, we combined experimental electron backscatter diffraction (EBSD) analysis with first-principles calculations to explore the crystal growth and faceting mechanisms of Ag3Sn intermetallic in solidifying Sn-xBi-1Ag (x = 10, 57 wt.%) alloys. Using EBSD techniques, accommodated for a pseudo-hexagonal setting of Ag3Sn to avoid pseudo-symmetry, and subsequent lattice transformation to an orthorhombic structure (a = 5.97 Å, b = 4.78 Å, c = 5.18 Å, Pmmn), this study reveals predominant (001)orth facets in Sn-10Bi-1Ag, and both (001)orth and more frequent (010)orth facets in Sn-57Bi-1Ag. Stability assessments of various crystal surfaces through first-principles calculations found the (010)orth surface to be most stable, followed by the (001)orth. Variations in stable facets between the two alloys may result from energy minimization influenced by atomic attachment at the liquid/solid interface, dynamic non-equilibrium solidification conditions, Bi concentration, and growth twinning. These findings enhance the understanding of intermetallic compound growth in solder alloys, with implications for solder joint technology improvement.