This study deals with the stability of a stratified structure composed of a cohesive and frictional overburden, a viscous substratum, and a rigid basement. That structure should be seen as a prototype for various salt tectonics and lithospheric plates stability analyses. The destabilizing factors are the density contrast, the tectonic compressive stress, and the possible erosion and deposition at the top surface. The overburden stiffness, a nonlinear function of in situ stress, has a stabilizing role. Two solutions are extracted from the variational formulation of the stability problem previously proposed [Leroy and Triantafyllidis, 1996]: the first is analytical and is obtained by disregarding gravity, and the second is numerical and is based on the finite element method. The latter is used to assess the validity of the previously presented asymptotic solution. It is shown that the asymptotic solution is accurate even for values of the small parameter, defined as the perturbation wavenumber times the overburden thickness, as large as 0.4. Furthermore, the possibility for the cohesive material in the overburden to accommodate part of the deformation by slip along a population of small pervasive faults is accounted for by the introduction of a deformation theory of plasticity. Stability predictions based on this theory indicate that structural modes, such as folding, and localized faulting modes are triggered for similar stress magnitudes. The parametric study presented includes the previously undetected influences of the stress gradient with depth and of the work hardening properties of the competent overburden. The role of erosion and deposition in destabilizing shallow overburdens, regardless of the magnitude of the tectonic stress, is also established. The stability predictions are then applied to a folded section through the Campos basin, offshore Brazil, revealing that the deformation theory of plasticity is necessary to explain the buckling that occurred during the Albian.