Salt structures are highly associated with economic hydrocarbon reservoirs. However, drilling a wellbore near or through the salt is usually difficult because the near-salt stresses and pore fluid pressures are largely perturbed due to weaker mechanical strength of salt bodies than their surrounding sediments. We have developed a 2D plane-strain poroelastic finite-element model to simulate stresses and pore pressures in the horizontal-compression salt tectonic system, the Kuqa depression in the Tarim Basin, China, and we use the model results of stresses and pore pressures to calculate safe drilling mud weights on drilling in the salt basin. We found that in early stage of the transient process (close to the undrained condition), pore fluid overpressure occurs at salt convex due to additional compression, whereas underpressure occurs at salt concave due to additional extension within the minibasin. Horizontal effective stress decreases at salt concave (within the minibasin) but increases at salt convex; vertical effective stress varies oppositely to horizontal effective stress. In the final stage of the transient process (drained condition), overpressure has dissipated and pore pressure remains hydrostatic, and stress perturbations are similar to those from the static geomechanical model with elastic sediments: horizontal stress increases at salt convex but decreases at salt concave; vertical stress slightly increases at salt convex and concave. Our calculated safe drilling mud weights and their windows vary over time. Especially at the salt convex, the safe windows are relatively narrow in the early stage of the transient process but become wider in later stage because overpressure dissipates over time and this makes drilling easier. Our results indicate different perturbation patterns of stresses and pore pressures near different salt geometries in a horizontal-compression salt tectonic system, and provide insights into wellbore drilling design and safe drilling mud weights in the salt system.