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Subducted slabs provide the primary driving force for mantle convection and plate tectonics. The strength of the slab directly controls the transfer of forces between it and the lithospheric plates at the surface. However, slab viscosity constrained by surface topography and gravity data is significantly lower than that suggested by mineral physics laboratory experiments. It is unclear whether the free-slip top boundary condition used by these studies affects the inverted slab viscosity. In this study, we constrain the subducting slab viscosity structure by comparing the computed topography and gravity in slab subduction models with a free surface with observations. The free-surface model results support relatively weak slabs (20–120 times more viscous than the upper mantle) at the bending region, consistent with previous studies with a free-slip top boundary. The viscosity of the slab below the bending region barely affects the surface topography and gravity field, and both strong and weak slabs fit the observed topography and gravity field, suggesting that extra independent observations are needed to constrain the deep slab viscosity. We investigate the comprehensive relations between subduction interface viscosity, surface topography and gravity anomaly, and trench motion. Models with trench advance have significantly low topography and gravity above the volcanic arc, contradicting subduction zone observations. Together with present trench motion observations and previous studies, we support the idea that the trench retreats under normal single-slab subduction conditions. • We constrain slab viscosity with topography and gravity anomalies in slab subduction numerical models with a free surface. • Model results support relatively weak slabs (20–120 times more viscous than the upper mantle) at the bending region. • Trench advance requires strong subduction interfaces, which result in significant arc depressions that contradict the observation. [ABSTRACT FROM AUTHOR]