We argue that the plastic rheology of the lithosphere, rather than its ''recoverable'' elastic properties, is responsible for the systematic development of periodic instabilities during compression or extension. We use a linear perturbation model with analytical solutions to calculate the instability modes for various rheologies. The growth of such periodic instabilities is enhanced by the highly nonlinear stress-strain rheologies encountered in the brittle layers of the lithosphere. On the contrary, ductile layers, deforming according to high temperature creep flow laws, tend to inhibit these instabilities. For oceanic domains, we assume that the only brittle layer is the upper part of the lithosphere. In compression, the only valid instability is a buckling whose wavelength is around 4 times the thickness of the brittle layer. Calculated wavelengths and growth rates are consistent with observations available for the Indian Ocean. For continental domains, a reasonable assumption is the existence of two plastic layers, one in the upper crust, the other in the upper mantle, for Moho temperatures between 450 ¿C and 600 ¿C. In compression and extension, two instabilities develop a long wavelength instability involving the whole lithosphere (coupling mode) and a short wavelength instability involving the crust and controlled by the upper brittle layer (intrinsic crustal mode). In compression, the coupling mode is a whole-lithosphere buckling, with a wavelength about 4 times the thickness of the active lithosphere (the two plastic layers plus the intermediate ductile layer). In extension, the coupling mode is a boudinage of opposite phase in the two plastic layers and a folding of the intermediate ductile layer. The intrinsic crustal mode is a crustal buckling in compression, crustal boudinage in extension. Neither deflects the Moho. The intrinsic crustal mode is favored by an increase in thermal gradient and by a decrease in strength of the ductile lower crust. ¿ American Geophysical Union 1992