The interaction of a supersonic plane or axially symmetric jet with a background gas of equal or different species is investigated in the transition regime between continuum and free‐molecule flow by solving a set of Boltzmann equations with simplified collision terms. In the solution, the discrete ordinate method is applied and extended to axially symmetric flow by introducing an approximation to the curvature terms. The rate of convergence of the solution is increased by using the deviations of the distribution functions from the equilibrium solutions as dependent variables. The results show that three flow regions characterized by the ratio of cross to self‐collisions can be identified in the jet structure. The penetration of the jet by background molecules is studied with regard to isotope separation. The influence of various assumptions for the boundary conditions on the solution is discussed. Density profiles computed for axially symmetric flow are compared with recent experimental data.