A series of analogue models were run to investigate oblique inversion of pre-existing grabens when overprinted by later shortening and the effect of these grabens on development of contractional structures. Obliquity angle (α) defining the initial trend of pre-existing grabens relative to the shortening direction, was systematically changed from 0°, 10°, 20°, 30°, 40°, 50°, 65° and 90°. Different structural styles are shown in different models and also in sections cutting across different parts of the models. Model results show that existence of multi-grabens enhances lateral discontinuity of overprinted thrusts in map view. With increasing the obliquity angle, more and longer lateral ramps developed sub-parallel to the graben trends. The pre-existing grabens were apparently rotated from their initial trends during shortening. Some of the normal faults bounding the grabens were partially inverted and resulted in bulging of the syn- and post-rift graben fill sediments. Most normal faults were displaced and rotated by thrusting, and provided relatively weak zones for propagation of thrusts. By comparing with observations from Qingxi graben in western China and from the SW Taiwan fold-and-thrust belt, where oblique inversion occurred, model results can be used to interpret unclear relationships between thrusts and pre-existing extensional structures during superimposed deformation.