Three-dimensional numerical models of asthenospheric flow and deformation in the oceanic lithosphere predict variability in the stress field that reflects the geometry of the ridge-transform boundary. A series of 3-D Boundary Element calculations shows how spreading rate, transform offset and segment length each influence the flow and stress fields that develop during plate-driven asthenospheric flow beneath a ridge-transform boundary. The predicted patterns of stress-supported seafloor relief generally follow those observed: median valleys are predicted at slow-spreading ridges vs no rift valley or, in some cases, a small axial high at fast spreading ridges; nodal deeps occur at ridge-transform intersections for offsets greater than 25 km; longer segments have more along-axis deepening than short segments which do not shoal much in their center. The predicted amplitude of the stress supported topography is up to 20% (across axis) and 40% (along axis) of that observed for an assumed asthenospheric viscosity of 5¿1019 Pa s and a weak lithosphere (local compensation).¿ 1997 American Geophysical Union