This contribution is concerned with the stability of a frictional, cohesive material layer, called the overburden, resting on a viscous, incompressible layer of lower density referred to as the substratum. The viscous layer is either perfectly bonded or free to slip with no friction on a rigid basement. The in situ stress is assigned a realistic gradient in the overburden and is assumed to be purely hydrostatic in the substratum. A general variational formulation of the linearized stability problem for the stratified system is obtained in which the viscous response of the substratum provides the characteristic time. To a given state of stress and perturbation corresponds a rate of growth or decay which is calculated by an asymptotic method for small overburden thickness compared to the perturbation wavelength. It is found that the substratum's thickness influences the rate of growth of the instability if its product by the perturbation wavenumber is smaller than 3 or 4, depending on the type of boundary condition at the basement. However, these conditions and the substratum thickness have no influence on neutral stability. Furthermore, the conditions for stability depend on the tectonic stress distribution in the overburden and not solely on the density contrast, as is the case for viscoelastic systems. It is also shown that the classical flow theory of plasticity adopted for the overburden, which successfully captures the onset of folding, fails to predict initiation of faulting for similar stress conditions.