Large rock inclusions are embedded in many salt bodies and these respond to the movements of the salt in a variety of ways including displacement, folding and fracturing. One mode of salt tectonics is downbuilding, whereby the top of a developing diapir remains in the same vertical position while the surrounding overburden sediments subside. We investigate how the differential displacement of the top salt surface caused by downbuilding induces ductile salt flow and the associated deformation of brittle stringers by an iterative procedure to detect and simulate conditions for the onset of localization of deformation in a finite element model, in combination with adaptive remeshing. The model set-up is constrained by observations from the South Oman Salt Basin, where large carbonate bodies encased in salt form substantial hydrocarbon plays. The model shows that, depending on the displacement of the top salt, the stringers can break very soon after the onset of salt tectonics and can deform in different ways. If extension along the inclusion dominates, stringers are broken by tensile fractures and boudinage at relatively shallow depth. Spacing of the boudin-bounding faults can be as close as 3-4 times the thickness of the stringer. In contrast, salt shortening along the inclusion may lead to folding or thrusting of stringers.