The longitudinal variations in the time-mean transport by the Brewer-Dobson circulation are studied using a three-dimensional (3-D) residual circulation approach to analyze the effects on zonal asymmetries in stratospheric ozone (O-3) and middle atmospheric water vapor (H2O). For January, the monthly mean residual winds, including both the Eulerian flow and the eddy-induced time-mean flow, were derived from general circulation model simulations with interactive chemistry (HAMMONIA), reanalysis (ERA-Interim), and satellite data (Aura/MLS). Extending the picture of the zonal mean two-dimensional Brewer-Dobson circulation, we find a 3-D circulation structure in relation to the zonal wave one in the middle atmosphere, including northward and downward residual winds over northern Europe/Asia with the downwelling directed toward the center of the polar vortex over northern Siberia, as well as southward and upward residual winds over the northern Pacific/Aleutians, and a pronounced cross-polar transport from Asia to North America in the middle stratosphere. The residual advection of O-3 and H2O shows that the observed wave one patterns in O-3 and H2O are produced by the zonal asymmetries in the residual mass transport in which Eulerian and eddy time-mean transports are largely counteracting. In comparison to observations, the model underestimates the effects of planetary waves but overestimates those of transient waves in configuring the stationary waves in O-3 and H2O. Overall, the 3-D residual circulation approach provides a useful diagnostic for understanding regional differences in middle atmospheric trace gas distributions and for validating general circulation models with interactive chemistry.