The cryogenic pumping system (CPS) is the last active tritium pumping system of the Karlsruhe tritium neutrino (KATRIN) experiment, in which the neutrino mass will be directly measured from the tritium beta decay. The spectrometer systems downstream to the CPS are required to be tritium-free. The high pumping speed of the CPS is to be provided by condensed argon frost at 3-3.5 K on the surfaces of the beamline tubes. In this unique design the beta particles can be simultaneously guided to the spectrometers by the superconducting magnets around the beamline tubes. In addition, nonevaporable getter (NEG) strips or NEG coated tubes are to be used in the last two sections of the CPS to secure this tritium-free boundary in case of a cryogenic failure event. In this article, the properties of the CPS are studied by the test particle Monte Carlo method, in which the effects of the argon frost sticking coefficient, the geometry of the beamline tube and the bend angle between two beamline sections are addressed. The tritium flow rate reduction factor and the adsorption distribution profile are estimated. The performance of the NEG section at different geometries is also presented. (C) 2008 American Vacuum Society.