A Monte Carlo computer code for analyzing free molecular gas flow has been developed to study the pumping characteristics of compound cryopumps for plasma chamber evacuation of fusion reactors. The code can deal with complex internal geometries of the pumps which commonly consist of cryopumping surfaces surrounded with elements like baffles, shields, and reservoirs. This code was used to study the pumping performance of a compound cryopump in the Tritium Systems Test Assembly (TSTA) at Los Alamos National Laboratory. The results show that the calculated pumping speeds are strongly affected by the geometrical models employed in the calculations, and that an analysis based on a detailed model is essential to estimate the performance of compound cryopumps. The TSTA pumps were recently updated and are expected to be tested and operated with actual mixtures of deuterium, tritium, and helium. Then the code will be used to interpret the measured pumping speeds.aPermanent address: R&D Center, Toshiba Corporation, 4–1, Ukishima-cho, Kawasaki-ku, Kawasaki, 210, Japan, (044) 277–3111.