Drilling into and around salt bodies can present different kinds of geohazards, such as shrinkage or stuck and crushed casings, resulting in well abandonment and huge economic losses. These engineering disasters are more likely to happen when ignoring the stress perturbations caused by the geomechanical interactions between the salt and surrounding sediments. For a better understanding of the stress perturbations, we use a commercial finite-element software, Abaqus, to build a 2D plane-strain finite-element model of the salt structure of Kuqa depression in the Tarim Basin and simulate the stress perturbations around the salt body in the environment of tectonic compression. By analyzing the patterns of stress perturbations due to different salt geometries such as concave and convex salt, we have come to the conclusion that the convex salt causes compressional stresses on the horizontal and out-of-plane directions but the extensional stress on the vertical direction. On the contrary, the concave salt induces extensional stresses on the horizontal and out-of-plane directions but compressional stress on the vertical direction. The results of stress perturbations near a salt structure in the environment of compressional tectonic stress are opposite to those in the environment of extensional tectonic stress, such as the Mad Dog, in the deepwater northern Gulf of Mexico. The shear stress () near the salt structure is bigger than those far away from the salt structure, but is much smaller when compared with horizontal, vertical, and out-of-plane stresses () in the profile, in the salt body, horizontal stress drops and converges to vertical stress and von Mises stress () equals to zero due to isotropic stresses. The results provide scientific insights on stress perturbations and wellbore drilling design near salt structures in the Tarim Basin.