The effectiveness of parallel plate arrangement as a cryogenic pumping device is examined by use of the direct simulation Monte Carlo method. The arrangement consists of two parallel plates and an end plate. The molecular beam is incident on the 80K plate cooled by liquid nitrogen. Molecules reflected on this plate are then incident on the opposite 20K plate cooled by liquid helium, where most of molecules are condensed. The percentage of non-condensing flux depends on various factors. The effect of the condensation coefficient, the density of incoming stream, and the geometry of the arrangement is examined.