Numerical solution of the Boltzmann equation with a relaxationcollision term is used to study gas-dynamic flows formed under nanosecondpulsed laser ablation. Atoms ejected from the surface of a target are assumedto have a Maxwell velocity distribution corresponding to the surfacetemperature and the saturated vapour pressure. The surface temperature isobtained from a transient heat transfer equation in the condensed phase.Atomic collisions in the ablation plume orient atoms towards the surfacenormal and speed up the plume expansion from the target. Atoms backscatteredin the gas phase, stick to the target surface and cause back condensation ofthe vapour at later stages. When the mean free path is much less than theplume dimension, a Knudsen layer, a hydrodynamic flow region, and alow-density tail may be distinguished in the gas phase. The present numericalsimulation is in good agreement with the analytical quasi-steady Mott-Smithapproach to the Knudsen layer in the case of evaporation and at the earlystages of condensation. Comparison with experiment reveals that the modelunderestimates both the width of the ablated material angular distribution andthe amount of high-energy atoms. The difference increases with the laserfluence and may be caused by lateral expansion of the plume, by vapouracceleration due to laser radiation absorption or probably by non-thermalevaporation effects.