A solid-on-solid model is proposed to describe faceting of bcc(1 1 1) metal surface induced by a metal overlayer. It is shown that the first-order phase transition occurs between faceted {2 1 1} or {1 1 0} and disordered phases. The ordered phases consist of large 3-sided pyramids with {2 1 1} facets or {1 1 0} facets. It is shown that the high-temperature disordered phase has not planar bcc(1 1 1) structure but faceted disordered structure. Hysteresis effects were observed when the system was warmed above the transition temperature and then cooled down. Temperature dependence of LEED patterns for faceted and disordered phase are calculated in kinematic approximation.