A finite element method with constrained elements and Lagrange multipliers is used to study tectonic faults in a viscous medium. A fault, representing the interface between overriding and subducting plates, has been incorporated into a viscous flow model of a subduction zone in which both thermal buoyancy and the buoyancy associated with the phase change from olivine to spinel are included. The fault causes stress to concentrate in its vicinity, giving rise to a weak plate margin and a mobile plate if a power law rheology is used. Surface dynamic topography with either a Newtonian or a power law rheology and with typical subduction zone parameters is characterized by a narrow and deep trench and a broadly depressed back arc basin. This suggests that oceanic trenches and back arc basins over subduction zones are dynamically compensated by viscous flow. Our models show that trench depth increase with fault dip angle, slab dip angle, slab length, and age of oceanic lithosphere just prior to subduction. The influence of fault dip angle and age of lithosphere on trench depth is greater than the influence of slab dip angle and slab length. These relationships of trench depth versus subduction zone parameters explain well the statistics of observed trench depths. For those subduction zones with oceanic lithosphere on both sides of the trench, observed trench depths have been corrected for fault and slab dip angles, based on the relationships from the dynamic models. After correction to a common set of parameters, trench depth correlates linearly with age of lithosphere prior to subduction with a slope which is close to what models having high viscosities within the transition zone and lower mantle predict. Comparison between the trench depths, corrected for fault and slab dip angles, and model trench depths suggests that the resisting tangential stress on faults in subduction zones may range from 15 MPa to 30 MPa, depending on model details. ¿ American Geophysical Union 1994