Previous work has suggested that the formation of folds, boudins, and mullions by creep is caused by the same general type of instability. The results of Newtonian flow models of this process compare poorly with observation, however. The study reported here extends the analysis to include a general class of non-Newtonian materials restricted only to being incompressible, anelastic (that is, without memory), isotropic, and homogeneous. Although the material is isotropic, the perturbation flow associated with growing structure is found to obey an anisotropic type of flow law. In a strain-rate softening material undergoing pure shear, resistance to additional normal straining is significantly reduced from the background level, whereas resistance to tangential straining is unchanged. This has a profound effect on the formation of geologic structures, increasing the growth rates and altering the dominant wavelengths. Non-Newtonian behavior turns out to be necessary for the formation of boudins and mullions and plays an important role, but not a necessary one, in the formation of folds.