The three-dimensional flow structures of cold dense overflow water on continental slopes with and without along-slope topographic variations and ambient slope water stratification are investigated, using a three-dimensional numerical ocean model. We discuss the effects of topographic steering and ambient stratification on the downslope transport of dense overflow on continental slopes. A constant upstream inflow of dense water is specified at the upper edge of the slope that represents an overflow from a marginal sea. We present the numerical simulations for overflow plumes in the presence of three topographic features: a cross-slope canyon that leads from the coast to the deep ocean, a cross-slope ridge, and a seamount. We compared the numerical results with the previously published results of overflow plumes on a uniform slope without ambient water stratification. In the presence of a canyon, a portion of the dense water descends into the canyon, forming a bottom-trapped plume that flows offshore along the right side (facing the ocean) of the canyon. The numerical result indicates that intensive mixing and entrainment occur in the canyon plume. The remainder of the overflow flows across the canyon and keeps descending on the slope while being deflected to the right-hand side of the inflow. In the presence of a cross-slope ridge, part of the water is blocked by the ridge and the flow is confined along the left side of the ridge. The remaining portion of the plume water flows over the ridge toward the right-hand side of the inflow. The presence of a canyon or a ridge significantly enhances the downslope transport of dense water compared with the uniformly sloping bottom case. A seamount does not affect the cross-isobath transport of dense water as much as does a canyon or a ridge. A seamount does influence the mixing, entrainment, and the plume trajectories. Ambient slope water stratification has significant influence on the mixing and cross-slope penetration of the overflow plumes. It has hindered the downslope penetration of the plumes as a result of enhanced mixing and entrainment when the plumes encounter deep denser water. ¿ 1998 American Geophysical Union