Large-scale periodic undulations within the oceanic and continental lithospheres revealed by a number of observations, are often treated as compressive instabilities, i.e. lithospheric buckling or folding. These undulations are normally associated with intensive faulting, which raises questions on the role of faulting in the folding process, and even on the possibility of folding in highly faulted media. In this study, we demonstrate that folding can "survive" faulting and that both processes may develop concurrently, so that faulting may serve as a mechanism of folding in the brittle domain. We support this hypothesis by direct numerical modeling. The results are compared with the data on three most prominent and well-known cases of the oceanic and continental folding-like deformation ("Indian Ocean" type, "Western Gobi (central Asia)" type and "Central Australian" type). We demonstrate that under reasonable tectonic stresses, folds can develop from faults cutting through the brittle parts of the lithosphere. The predicted wavelengths and nite growth rates are in agreement with the observations. We also show that within a continental lithosphere with thermotectonic 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.