Back-arc extension takes place in the overriding plate in an overall convergent setting during retreat of the hinge-line of the subducting slab. A large number of back-arc basins display a geometry and internal structure that is asymmetric, i.e. where the amount of extension increases from one end of the arc to the other. We present the results of 3-dimensional analogue modelling of asymmetric back-arc extension of an overriding lithosphere with a varying initial rheology. The results show that with increasing lithospheric brittle to viscous strength (BS/VS), the fault density decreases in magnitude, while the asymmetry in deformation pattern in the back-arc region increases. The area extent of deformation is mainly dependent on the ratio of brittle strength to buoyancy force (BS/BF), i.e. the larger the ratio, the smaller the area of deformation. The experimental results have been compared with several arc - back-arc systems, which display a relatively large amount of structural asymmetry (Tonga Arc, Kuril Arc, New Hebrides Arc, Ryukyu arc) but a varying style of tectonic deformation. These differences are mainly the result of the stage of opening up of the back-arc basin, the subduction setting (ocean-ocean or ocean-continent) and difference in rheology of the overriding lithosphere.