The distribution function at a point in a highly rarefied gas flow in a circular tube is shown to be made up of three parts which depend on whether reversed particle trajectories through the point strike the tube wall or pass into the chambers at the ends of the tube. The distribution function is applied to the calculation of the velocity profile development along the length of the tube. It is found that the most rapid changes in the velocity profile occur near the tube inlet. For longer tubes, there is a substantial length in which the velocity profile is fully developed. In general, the velocity profile is quite flat and this characteristic is accentuated for longer tubes. Some numerical information is also given for the distribution of the particle density throughout the flow. The determination of other local quantities is discussed and illustrated.