The mechanisms controlling mountain building at subduction zones remain debated. In particular the interaction between mantle flow and subduction has been poorly addressed while fundamental in controlling plate displacement and deformation. Here, we conduct three-dimensional analogue models at the scale of the upper mantle adding a horizontal mantle flow, so that plate displacement is not imposed as in most models, but is rather controlled by the balance of forces. We simulate three scenarios: no mantle flow (slab-pull driven subduction), mantle flow directed toward the subducting plate, and mantle flow directed toward the overriding plate. In that last scenario, we test the influence of pre-existing rheological contrasts in the upper plate to best reproduce natural cases where structural and rheological inheritance is common. Our experiments show that when plate convergence is also driven by a background mantle flow, the continental plate deforms with significant trench-orthogonal shortening (up to 30% after 60 Myr), generally associated with thickening. The upper plate shortening and thickening is best promoted when the mantle flow is directed toward the fixed overriding continental plate. The strength of the upper plate is also a key factor controlling the amount and rates of accommodated shortening. Deformation rates increase linearly with decreasing bulk strength of the upper plate, and deformation is mostly localized where viscosity is lower. Finally, we discuss the limits and strengths of our model results through a comparison to the Andes which are the best modern example of mountain building in a subduction context.