The effect of bottom topography H on the barotropic transport in a periodic zonal channel is studied. An asymptotic approximation is found for the zonal transport on an f-plane and a β-plane when all f/H isolines are blocked by the zonal walls. It is shown that to leading order, the zonal channel transport is independent of friction. In this it is similar to the Sverdrup transport in a basin. To leading order, the transport is proportional to the bottom topographic wavelength, and inversely proportional to the height of the topography and to R, the range of values of f/H that exists on both sides of the channel. For sufficiently high topography the transport varies inversely with the topographic height squared. The analytic results are verified by numerical experiments.