Peak-stress zones and pressure anomalies around wellbores through moving salt bodies threaten well integrity. Our study provides a conceptual framework to identify the depth of peak zones of shear stress in moving salt sheets, whether autochthonous or allochthonous. We use analytical methods to determine the principal stress magnitudes and stress-trajectory orientations caused by ductile creep in crystalline salt. The four basic flow types analyzed are Couette, Poiseuille, no-slip squeezing, and free-slip squeezing flow. The analytical formulae specify velocity gradients, shear-stress profiles, and principal stress trajectories. The analytical results are compared with detailed flow visualizations in numerical and physical models of salt tectonics to test our generic conclusions. We offer guidelines to optimize drilling operations in moving salt bodies. The study suggests that stress trajectories and zones of viscous stress peaks in salt layers should be mapped routinely during well planning, in addition to the traditional analysis of elastic stresses and safe mud-pressure windows for controlling wellbore stability.