A number of observations reveal large periodic undulations within the oceanic and continental lithospheres. The question if these observations are the result of large-scale compressive instabilities, i.e. buckling, remains open. In this study, we support the buckling hypothesis by direct numerical modeling. We compare our results with the data on three most proeminent cases of the oceanic and continental folding-like deformation (Indian Ocean, Western Gobi (Central Asia) and Central Australia). We demonstrate that under reasonable tectonic stresses, folds can develop from brittle faults cutting through the brittle parts of a lithosphere. The predicted wavelengths and finite growth rates are in agreement with observations. We also show that within a continental lithosphere with thermal age greater than 400 My, either a bi-harmonic mode (two superimposed wavelengths, crustal and mantle one) or a coupled mode (mono-layer deformation) of inelastic folding can develop, depending on the strength and thickness of the lower crust. ¿ 1999 American Geophysical Union