Many active compressional belts contain examples of transverse rivers intersecting anticlines at their highest structural and topographic position. This unusual association between rivers and doubly plunging anticlines at relatively small scales is usually explained by some form of antecedence or superposition. In this article I suggest an alternative explanation, i.e., that river erosion unloads the crust and that this process causes local deformation to be enhanced in the vicinity of rivers. I show the plausibility of this hypothesis with the aid of a coupled three-dimensional mechanical-surface process mathematical model. The conclusion is that river incision can have a major influence on deformation of the surrounding crust if incision occurs at the same time that the crust is deforming plastically in response to regional compression. In this case, incision amplifies background deformation at a relatively small scale, leading to the formation of noncylindrical folds with culminations coinciding with river incision. In the absence of regional deformation, the response of the crust to river incision is small and of long wavelength because it is governed by flexural isostasy of relatively rigid elastic crust. Thus, whether rivers exert an influence on local deformation depends critically on the timing between river incision and regional deformation. This point may explain why in some cases, rivers appear to have had no significant influence on local deformation, whereas in other cases, they have.