In many materials, crystalline interfaces are facetted. The experimental evidence is that on each side of an interfacial ledge, or along the facets meeting along a common line, low energy atomic structural units are preserved which accommodate elastically angular or/and length misfit(s). Each facet can be considered as a Somigliana dislocation (SD) whose core is extended on the facet. The elastic displacement field of a SD is derived in an anisotropic continuum, for any orientation of the facet relative to a given Cartesian frame. From an atomic point of view, the translation state of the two crystals on each side of the facet is defined. The dislocation content attached to a ledge or a dihedral angle formed by two joining facets along a common side is also analyzed. The local elastic field related to these cases are derived and applications are presented for depicting the positions of the atomic columns in theoretical plots. Comparisons are made with some other theoretical works and HRTEM images. Examples illustrate the application of the Somigliana model to grain boundaries in hexagonal crystals (Mg, WC), and an interphase interface Ni3AI/Ni3Nb.