The transmission probabilities and the number of molecules reflecting from the wall were computed using a Monte Carlo method for Free molecule flow through a conduit containing an orifice of zero thickness. The computed transmission probabilities were compared with a composite transmission rule and a series-resistance equation. The distribution of the molecular number density on the conduit wall along the conduit axis was determined by assuming that the ratio of the molecular number flux reflecting from the conduit wall to that entering into the conduit inlet corresponds to the ratio of the molecular number densities at each position. When the orifice was placed halfway down the length of the conduit, the composite rule and the series-resistance equation, respectively, agreed well with the computed transmission probabilities For tile conduits with the aspect ratio L/R greater than or equal to 10, and the cross-sectional area ratio of tube and orifice opening beta greater than or equal to 10, and for the conduit with beta greater than or equal to 40. The molecular number density distributions were symmetric with respect to the midpoint, and had a minimum in the upstream side and a maximum in the downstream side. The molecular number density distributions exhibited jumps across the orifice, as well as at the inlet and exit of the conduit.