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 (O3) 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 O3 and H2O shows that the observed wave one patterns in O3 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 O3 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.