An exact treatment of the stability of multilayered viscous fluids in slow motion with large deformations leads to an analog model which includes the effect of gravity. A distinction can be made between true mechanical instability and an apparent instability of purely kinematic nature. A mechanism for concentric folding is derived, leading to predictions in good agreement with experimental results (De Sitter, 1939). Exact equations are obtained for the time history of viscous buckling of multilayered fluids for small deflections superimposed upon a large variable compressible strain. A numerical application to the single embedded layer checks the practical validity of the simplified thin-layer theory with interfacial slip. For gravity instability, the analog model provides a method of analysis applicable to very large deformations in salt structures.