Monoclinal flexures, which are isolated asymmetric flexures, range in scale from a few millimetres in kink bands to hundreds of metres in monoclines on the Colorado Plateau. A general model of monoclinal flexuring of multilayers is proposed here; the multilayers include layers with various rheologies, densities, thicknesses, and strengths of contacts between layers. The multilayers are subjected to displacements at their base, stresses at their edges, and a free surface at their tops. We study in detail three modes of this general model, assuming linear, incompressible elastic or viscous multilayers: Drape folding, in which a monoclinal flexure develops over a...