A mathematical study of the flow of a layered fluid shows that homogeneous pure shear aligned with the bedding is a “possible” state of motion in the sense that it is an exact solution to the governing equation. In the case of a single layer of a Newtonian material between two thick layers of different viscosity, such a state of motion is unstable to small disturbances. The growing disturbances have foldlike or pinch-and-swell form, depending on whether the applied compression is parallel or perpendicular to the layering and on whether the layer is more or less resistant to deformation than the surrounding rock. The combination of these two factors gives four distinct cases. One of these, labeled inverse folding, is of no interest because its growth rate is too small. The other three cases correspond qualitatively to folding, boudinage, and mullions. This result suggests that these three geologic structures are caused by the same mechanism: a secondary flow driven by an interfacial discontinuity in normal stress.