Continuum models are used to investigate the large-scale deformation associated with the subduction of aseismic ridges. Formulated in the horizontal plane using thin viscous sheet theory, these models measure the horizontal transmission of stress through the arc lithosphere accompanying ridge subduction. Modelling was used to compare the Tonga arc and Louisville ridge collision with the New Hebrides arc and d'Entrecasteaux ridge collision, which have disparate arc-ridge intersection speeds but otherwise similar characteristics. Models of both systems indicate that diffuse deformation (low values of the effective stress-strain exponent n) are required to explain the observed deformation. Deformation is somewhat insensitive to the vertically integrated strength of the arc (inversely proportional to the Argand number Ar), but indicates that the arc lithosphere is not extremely weak (Ar < 100). Low values of both Ar and n suggest that the thermal structure is typical of ‘cold’ or ‘normal’ arcs and that deformation is dominated by flow in the lower crust and mantle. In addition, low values of n (approaching Newtonian flow) may indicate that specific deformation mechanisms dictate deformation of the arc lithosphere. Possible mechanisms include low-stress, grain-size dependent creep, pyroxenite-controlled rheology and mechanisms associated with water weakening. Changes in the boundary conditions greatly affect deformation within island arcs. High rates of arc-ridge intersection speed (Tonga-Louisville system) yield arc-parallel tension and crustal thickening in the wake of ridge subduction. In contrast, low rates of arc-ridge intersection speed (New Hebrides-d'Entrecasteaux system) yield compressional deformation directly arcward of the collision zone and transverse strike-slip faulting adjacent to the region of compressional deformation. Localized regions of extensional deformation along the frontal part of the arc adjacent to the collision zone may contribute to the formation of re-entrants.