Experimental investigation and computer simulation of a graphite monolayer (graphene) on different Ni single-crystal surfaces have been performed. In contrast to graphene on Ni(111), which forms a solid coating with a (1 × 1) structure, graphene on Ni(110) forms a complex crystal structure which is substantially distorted by interaction with the substrate. The calculations showed that the strong chemical interaction of carbon with nickel leads to a significant bending of the graphene layer (up to few angstroms). The calculated model made it possible to predict the main result of studying graphene on faceted surfaces, which revealed the graphene ability to coat geometrically nonuniform surfaces with a curved continuous film.