A general solution of the linearized Boltzmann equation with the Bhatnagar‐Gross‐Krook model for the problem of a rarefied gas flowing between two parallel, infinite plates is developed based on the discrete ordinate method. Analytic expressions of the perturbed distribution function, the velocity profile, and the gas volume flow rate, particularly suitable to numerical calculations, are thus obtained. These make possible obtaining the numerical solutions to any desired degree of accuracy. The results are compared with the analytical solutions of the half‐range moment method and with the numerical solutions of Cercignani.