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S U M M A R YAlthough subduction plays a dominant role in plate tectonics, related processes such as trench migration are not well understood. We investigate the influence of viscosity stratification and different flow boundary conditions on the trench migration dynamics of a subducting lithosphere in a 2-D model using a finite-difference code. Subduction and mantle flow are driven by a compositionally prescribed density contrast between the high-viscosity slab and the ambient mantle; no overriding plate is assumed. The model rheology is viscoplastic at shallow, and viscous at greater depth; the mantle is stratified with a higher viscosity in the lower part of the computational domain. The plastic rheology allows the plate to decouple from the top of the box and is described by a simplified friction law to mimic the brittle deformation of the shallow lithosphere. The flow patterns and slab morphologies differ as a function of the velocity boundary conditions (BCs). For reflective BCs, we model either a plate which is fixed on the box side or a plate that can freely move. A slab with periodic BCs is always laterally free. We find that, when the slabs interact with the highly viscous lower mantle, the slab with reflective BCs is more folded than the periodic one, due to the confinement of mantle flow around the slab. In general, the trench is observed to roll back toward the oceanic plate. For free slabs with reflective BCs the trench retreat velocity deceases after the interaction with the lower mantle. In contrast, for the free slab with periodic BCs it is nearly constant or even increases with time if described in a reference frame fixed to the lower mantle. The free slab with periodic BCs exerts a force on the lower mantle, which causes a net differential flow between the upper and lower mantle. We also carried out additional experiments with different mechanical slab properties and thicknesses. Stiffer, free slabs subduct more steeply and are able to penetrate straight into the lower mantle. After penetration into the lower mantle the trench moves toward the continent. Thinner slabs deform more easily and are folded for all boundary conditions. We can generalize the rollback systematics for free slabs by normalizing trench velocities by the plate speed. Free slabs, being more representative of the West Pacific subduction zones, show large temporal variations of normalized trench velocities ranging between a retreat value of 1.0 to an advancing value of −0.3.