The understanding of the interactions between subduction‐induced mantle flow and background mantle flow (being global or regional) remains incomplete despite its potential impact on subduction dynamics and associated deformation. Here we present the results of three‐dimensional laboratory models of subduction zones at the scale of the upper mantle in which we systematically vary the plate's width and trench perpendicular background mantle flow. In particular, we test different mantle flow magnitudes and directions of flow and evaluate their impact on the slab geometry in the vertical plane, trench shape evolution and the superficial horizontal mantle deformation. While the chosen viscosity ratio between the convective mantle and the subducting plate in our models (∼100) is favorable to the deformation of the slab through mantle displacement, we show that the geometry of the slab in the vertical plane is only marginally affected by the imposed background flow. Instead, the background flow has a larger impact on the horizontal kinematics and deformation of the trench. It reduces along‐trench variations of trench kinematics, which in turn decreases trench curvature, and it largely disturbs the pattern of mantle deformation at slab edges, inhibiting the development of toroidal cells. We also show that the thickness of the convective layer (here the upper mantle) controls the toroidal component of the mantle flow and the length scale of trench curvature for large subduction zones.