Along convergent boundaries, the role played by mantle drag remains poorly understood despite its potential impact on subduction dynamics and in turn on the deformation regime of the overriding plate. In this study, we present 11 three‐dimensional analog models of subduction including an overriding plate, in which mantle drag at the base of the lower or upper plate results from an imposed unidirectional horizontal mantle flow perpendicular to the trench, and in which the plate opposite to the flow is fixed. We varied the direction and the velocity of the imposed horizontal mantle flow between 0 and 10 cm/yr to quantify its impact on horizontal and vertical upper plate deformation, velocities of plates and subduction, and slab geometry. In our experiments, we show that a mantle flow lower than 5 cm/yr tends to laterally translate the slab rather than to generate internal deformation, resulting in limited differences in slab geometries between models. We also show that plate velocity correlates linearly with the imposed mantle flow velocity and associated mantle drag. The upper plate most often deforms by trench‐orthogonal shortening, with shortening rates increasing linearly with mantle flow. Shortening rates are higher when mantle flow is directed toward the fixed upper plate and when the slab has not yet reached the upper‐lower mantle discontinuity. Minimum trench‐orthogonal shortening rates of 2.5 × 10 −15 s −1 are required to thicken upper plates. This study suggests that mantle drag can exert first‐order controls on the dynamics of subduction zones and associated tectonics.