The ocean general circulation model of the Geophysical Fluid Dynamics Laboratory has been modified to accommodate a generalized vertical coordinate transformation. The model with a slightly modified &sgr; transformation (&sgr;=z/H) is applied to three simple test cases. A clear improvement of barotropic and barolclinic topographic Rossby waves has been achieved compared with the z-coordinate model. A somewhat more typical time-independent problem for the overflow of dense water masses over a zonal ridge exhibits the potential benefits as well as the flaws of the new model. Vertically integrated mass transport is very sensitive to changes in bottom slope in regions where planetary and topographic β are of comparable magnitudes. This translates into large errors in the z model due to the crude approximation to the actual topography. The deep flow in the z model does not follow the bottom exactly. Horizontal overshoots of dense water lead to convective mixing on the southern side of the ridge. This can be a serious problem for modeling more realistic overflow situations with the z model. Increased diapycnal diffusion has been identified as the most serious problem with the terrain-following coordinate system for this specific application. ¿ American Geophysical Union 1993