The Havre Trough is opening by oblique back-are rifting which is propagating into the continental margin of New Zealand at the Taupo Volcanic Zone. Variations of deformational style along the rift axis have been investigated by comparison with analogue experiments which incorporate brittle and ductile rheologies and are scaled for gravity. Based on the results of the analogue experiments, we present a tectonic model for oblique rifting in the Havre Trough, which involves the rheological contrast between oceanic and continental lithosphere and the oblique geometry of the continental margin of New Zealand with respect to the regional rift trend. The model shows that the continental margin, which is weaker than both oceanic and continental lithosphere, cannot support large shear stresses. The two lithospheres can be decoupled during extensional events along the marginal shear and, depending on the continental margin orientation, this shear can modify the regional stress field. A heterogeneous stress field will rotate normal stresses to be perpendicular or parallel to the margin. As the two lithospheres decouple during extension, the rift grabens and internal faults of the oblique rift system propagate normal to the marginal shear. This model explains the oblique trend of the Havre Trough's tectonic fabric and its relationship to the Vening Meinesz Fracture Zone which represents the oceanic/continental lithospheric boundary. As the Havre Trough rift propagates into the continental margin; rheological differences between oceanic and continental lithosphere result in variations in distribution of strain along the rift axis. Extension of oceanic sub-are lithosphere is localized into a single rift graben. At the transition into continental rifting, the zone of extension widens into a number of rift grabens forming complex indentations into the margin. This change in deformation style is consistent with analogue experiments as well as other natural examples and results from the contrast in lithospheric rheology and its influence on the process of strain localization.