Flexural flow produces a continuous deformation equivalent to that of a flexed deck of cards of vanishing card thickness. It is assumed to be a common process by which parallel folds are formed in nature in competent, anisotropic rock layers. The strain pattern produced by flexural flow contrasts strongly with that produced in parallel folds formed by the bending or buckling of isotropic competent layers, but it has not been documented in nature. Two basic questions are thus: (1) If anisotropy is sufficiently large, will flexural flow develop, and (2) if so, are competent rocks sufficiently anisotropic for them to respond to deformation by flexural flow? A measure of planar anisotropy, A, is given by the ratio of viscosity in shortening to viscosity in shear. Finite-element modeling indicates that if the value of this ratio is greater than about 50, the strain pattern in a buckle fold in a competent layer will be almost indistinguishable from one of flexural flow. Such a high anisotropy, however, is unlikely in natural competent layers. The most texturally anisotropic rocks tend to be those rich in phyllosilicates, and these usually behave in an incompetent fashion. Common competent rocks, such as those rich in quartz and feldspar, are rarely significantly anisotropic. A strong preferred crystallographic orientation as a result of crystal-plastic flow can produce anisotropic layer behavior, but A is unlikely to exceed ∼10, which is insufficiently great for folding by flexural flow. We thus conclude that flexural flow is unlikely in single competent layers. The aggregate response to deformation, however, of composite layers of alternating competent and incompetent rocks may be highly anisotropic and on average correspond to flexural flow.