Abstract An idealized bilaminate multilayer of alternating ‘competent’ and ‘incompetent’ layers with different proportional thicknesses is used to model theoretically the manner in which flow in rocks may vary from layer to layer during deformation. The layers are assumed to flow according to a ‘power law’, with stress exponent ( n) of 1 (=Newtonian flow), 3 or 5, which is in accordance with current experimental data for flow in rocks. The theoretical analysis concentrates first on incompressible plane flow, and is then extended to some forms of incompressible three-dimensional flow. Strain-rate variations from competent to incompetent layers are illustrated for two-dimensional flows on ‘rheology graphs’ of log stress vs log strain-rate. Three types of bulk multilayer deformation are illustrated: layer-parallel pure shearing (LPPS), layer-parallel simple shearing (LPSS) and layer-oblique straining (in different orientations). The degree of flow partitioning varies with the bulk flow, layer thicknesses, and layer n values. For all systems in plane (two-dimensional) flow, the greatest partitioning occurs for 45° bulk shortening (LPSS), and is most extreme for high n values, such that the strain-rate is virtually zero in competent members. However, for three-dimensional flows, preliminary results suggest that the value of n may play a less significant role in flow partitioning, particularly for bulk pure flattening or constrictional flows. These theoretical flow variations provide some meaning to ‘competent contrast’ in rocks, and reveal possible links between relative competence and deformation history. Such flow variations in space and time may provide the driving mechanism for folding in ductile multilayered systems.