Macroscopic constitutive relations of solid-liquid composites are derived as functions of microscopic geometry described by grain-boundary contiguity. The model consists of solid grains, which make a framework through grain-to-grain contact, and an interstitial liquid phase. Contiguity is the essential geometric factor that determines the macroscopic mechanical properties of the granular composites, while the other factors such as liquid volume fraction affect the properties only indirectly through the contiguity. Contiguity is defined by the portion of the grain surface being in contact with the neighboring grains, and takes a value between 0 and 1. Total length of the solid-solid and solid-liquid phase boundaries observed in cross section can be quantitatively related to the contiguity. Contiguity &phgr; can be extended to a tensor &phgr;ij to cover anisotropic grain contact. The full anisotropic macroscopic elasticities are quantitatively derived as functions of contiguity. Also, as an attempt to apply the present formulation to viscous behaviors of solid-liquid composites, bulk and shear viscosities are derived as functions of contiguity. The results successfully predict the large structural sensitivities of these properties; the bulk and shear moduli (or viscosities) of the skeleton are drastically reduced by decreased contiguity and vanish when contiguity vanishes. For partially molten media under thermodynamic equilibrium, geometrical variation according to melt fraction and dihedral angle is quantitatively related to the variation of contiguity, and the acoustic properties are derived as functions of melt fraction and dihedral angle. ¿ 1998 American Geophysical Union