The equilibrium distribution of a fluid phase in a rock is controlled by the ratio of grain boundary energy to solid-fluid interfacial energy (surface energy). A strong dependence of interfacial energy on interface orientation (anisotropy) is the rule for solid-fluid surfaces of geological interest. We investigated the effects of surface energy anisotropy on the equilibrium interface configuration at the junction of two crystals with a fluid in a two-dimensional solid-fluid system. The two major effects are to promote the development of planar solid-fluid interfaces parallel to crystallographic planes of minimum energy and to lead to large variations of the dihedral angle from one triple junction to the other (as a function of the orientation of crystalline lattices relative to the grain boundary). Despite these large variations, the frequency distributions of equilibrium dihedral angles remain unimodal; also the relationship between the mean fluid dihedral angle and the ratio of grain boundary to surface energy is very close to the isotropic law. Even in the most anisotropic systems, the fluid dihedral angle is therefore a parameter of primary importance for predicting the grain-scale geometry of a low-volume fraction of fluid and its mobility. ¿ 2001 American Geophysical Union