Sedimentary rock folding results from a number of mechanisms, including buckling due to lateral tectonic compression and slip on thrust faults in the underlying strata. Movements experienced by folded layers are typically very large and may include significant rigid body translation and rotation, considerable straining, and relative slip at the interface between layers. In this paper we present a mechanical model for capturing isothermal ductile folding processes of sedimentary rocks using nonlinear continuum mechanics and finite deformation contact kinematics. Folding of rock layers with distinct mechanical properties may result in relative tangential slip at the interface between them. Of particular interest is the formulation and implementation of a finite deformation frictional contact model to account for relative sliding of two adjacent rock layers. Our method considers a Coulomb friction law that is suitable for geomaterials. The penalty method is used to implement the frictional contact model [
]. The formulation of the model includes a consistent linearization of the weak form of the linear momentum balance to enable optimal convergence for Newton-Raphson iterations. To capture the ductile response of the rock layers, we implement an elastoplastic constitutive model; a three-invariant yield criterion is used to define plastic loading and a non-associated flow rule to control inelastic dilatancy. To integrate the stresses we employ a fully Lagrangian approach along with multiplicative plasticity theory for finite deformations. This work enables us to investigate the relationship among folded shapes, internal stress state, and the occurrence of deformation bands and/or relative slip at the layer interfaces. Supported by U.S. Department of Energy, Grant No. DEFG02- 03ER15454, and U.S. National Science Foundation, Grant No. CMG-0417521.