An equivalence between generalized restricted solid-on-solid models, associated with sets of graphs, and multi-colour loop models is established. As an application the authors consider solvable loop models and, in this way, obtain new solvable families of critical RSOS models. These families can all be classified by the Dynkin diagrams of the simply laced Lie algebras. For one of the RSOS models, labelled by the Lie algebra pair (A_L,A_L) and related to the C₂⁽¹⁾ vertex model, they give an off-critical extension, which breaks the Z₂ symmetry of the Dynkin diagrams.