A kinetic theory analysis is made of the flow of a rarefied monatomic gas through a two‐dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete ordinate methods. The former method portrays the transition regime characteristics well, but has limitations in the free molecule regime. The latter method gives accurate results in the free molecule and slip regime and bolsters confidence in the accuracy of the transition regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytic solution of the moment equations for length‐to‐width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.