The Poiseuille flow of a rarefied gas between two parallel plates is analyzed numerically for an inverse Knudsen number ranging from 0 to 10.5. The Bhatnagar, Gross, and Krook model is used and the transport integrodifferential equation is reduced to a purely integral one, which is solved numerically by the discrete ordinate method.The plot of the volume flow rate vs pressure is shown to have the expected minimum; besides, it fits well with experimental results and previous approximate calculations.In particular, the results given by Takao, properly corrected, are in good agreement with ours.