Lithosphere extension and continental breakup axes are often (sub-) parallel to orogenic belts and suture zones. In an attempt to understand the relation between weak zone orientation and extension direction, a 3-D numerical model is developed with which the following aspects are studied: the relation between weak zone axis and axis of maximum crustal deformation, the amount and distribution of crustal thinning, and subsequent implications for rift (a)symmetry. The results suggest that upon oblique extension, rifts develop within the weak zone that individually cross the inherited structure, while as a group they follow the weak trend. This results in an alternating rift asymmetry; the pattern of crustal thinning, topography and thermal structure are not symmetric around the rift axes of the major rift zones and change along-axis over such a rift. This is a possible explanation for alternating asymmetric rift structures such as observed in the East African Rift system.