A competent layer with a nonlinear rheology can, under extension, exhibit pinch-and-swell instabilities. Such instabilities can explain small-scale regular deformations of rock. Recently they have also been invoked in relation to the distribution of basins and ranges (Fletcher and Hallet, 1983) and the undulation of the Bouguer map (Froidevaux, 1986) in the western part of North America. For the case of a simple stratified structure, different authors have expressed mathematical solutions describing these instabilities. In this paper we elucidate the general physical meaning of these nonhomogeneous deformations. In the simplest case where the competent layer is fully embedded in a softer material, a fundamental mode develops with a preferred wavelength equal to 4 times the thickness of a competent layer. The novelty is the occurrence of overtones with alternate symmetrical and antisymmetrical deflections of the interfaces between layers. These modes have a large amplitude when the rheology tends to perfect plasticity. The presence of a free surface like the earth's surface for the upper crust is shown to double the preferred wavelength of the fundamental mode and to forbid one overtone out of two. This new effect is caused by gravity which inhibits the growth of surface topography. Another shift is of opposite sign to that caused by a free surface. Numerical solutions for multi-layer structures can elucidate the nature of couplings between various layers. The case of a three-layer lithosphere having a soft lower crust and overlying a mantle asthenosphere has been analyzed in some detail. It shows that, in the range of wavelengths larger than 30 km, up to five preferred modes may be superimposed. This should encourage further analysis of the western U.S. topography and gravity pattern which is known to contain at least two wavelengths: about 40 km for the individual basins and ranges and about 200 km for the Bouguer troughs in Nevada and their associated broad topographies.