Theoretical analyses have been conducted dealing with free-molecule gas flow through tubes and two-dimensional slots. Diffuse reemission from the walls has been assumed. Models investigated include converging and diverging slots and tubes as well as parallel-walled slots and cylindrical tubes. For the parallel-walled slots and cylindrical tubes, effects of both free-molecule flow and surface diffusion were studied. The results are summarized in this report. The pertinent integral equations, developed from classical kinetic theory are presented as are other important relations covering various transmission factors.