We study the development of finite amplitude folding of the lithosphere through the application of finite element models characterized by both discontinuous (layer over half-space) and continuous (strength envelope) viscosity distributions. Both models include strongly strain rate-dependent rheologies that approximate slip on pervasive faults. Folding with layers of uniform, contrasting viscosities is driven solely by the magnitudes of discontinuities in viscosity at layer interfaces; however, folds may also develop in a medium with a continuously varying viscosity distribution. The net driving force for folding in a region of continuous viscosity variation is the same as the driving force across a discontinuity with the same net viscosity contrast. Continuous and discontinuous viscosity variations give essentially identical fold growth rates if the depth over which the viscosity varies is small compared to the wavelength of folding or the depth of the viscosity variation. In the uniform viscosity layer model, flexural bending of the layer results in a state of extension on topographic highs and compression in topographic lows. In contrast, the strength envelope model is characterized by significant penetrative shortening near the surface that results in a state of compression everywhere along the fold. This model predicts layer thickening beneath fold troughs, as observed in the intraplate deformation zone in the central Indian Ocean. Buoyancy forces retard the rate of fold amplification but are inadequate to prevent folding for a range of realistic lithospheric rheological structures. ¿ American Geophysical Union 1996