Theoretical analyses of the stresses, displacements, and stress trajectories associated with faulted drape-folds are obtained for two boundary-value problems in linear elasticity. Two different conditions — welded and frictionless — are assumed for the interface between the overlying sedimentary veneer and the forcing basement rock. In nature the situation lies somewhere between these two extremes. Solutions are obtained for impulsive boundary conditions in the stresses and displacements; the solutions for spatially-varying boundary stresses and/or displacements are obtained from these by the convolution theorem. Consequently, the stresses, displacements, and stress trajectories in the sedimentary veneer can be determined for boundary stresses and/or displacements that may be non-analytic functions of position. The stress trajectories compare well with those determined by previous petrofabric analyses of experimentally deformed rock specimens. Potential faults are predicted from the calculated stress trajectories and the Coulomb-Mohr failure criterion. They are compared with those observed experimentally, and the correlations are good, even though the experimental faults have relatively large displacements. This suggests that the stress patterns established in the early (linearly elastic) stages of deformation strongly control the later stress patterns and, consequently, the sense of displacements along the faults.