Abstract: The internal deformation of the Appalachian Plateau décollement sheet has a distinctive style involving kink bands and thrusts. In areas where the décollement sheet is underlain by thin salt, the dominant structures are thrusts developed at shallow levels, underlain by a series of steep kink bands that terminate downwards at the Silurian salt décollement. Where the salt is thick, large asymmetrical anticlines developed with hinterland-verging kinks on their back-limbs that deformed the entire supra-salt sequence. In order to understand the constraints on deformation, we have used analytical mechanical modelling based on the maximum strength theorem. The simplified model consists of three layers: two are fluids and the third, intervening layer is a stratified competent material. The model is compressed horizontally and the predictions made are based on the kinematic approach of classical limit analysis. Two modes of deformation are investigated: the thrust and the kink band. The modelling shows that kink bands dominate deformation at large burial depth. At shallower depth and small regional bedding dip, the dominant mode is thrusting. In areas of open folding it is predicted that through-going hinterland-verging kink bands will form at a critical limb dip angle of about 10°. Supplementary material: Technical details of the mechanical theory behind this article are available at https://doi.org/10.6084/m9.figshare.c.3799492