Abstract The method of discrete ordinates for the solution of the Boltzmann equation simplified by the BGK-model is extended to cylindrical coordinates. The curvature terms of the model equations are approximated by means of an ellipsoidal distribution function. The model equation is solved by means of finite-difference approximations. The rate of convergence of the iterative procedure employed is shown to be accelerated by introducing the deviation of the distribution function from a Maxwellian distribution into the model equation. To illustrate the applicability of the method, results are reported for the flow of an axisymmetric jet in a finite-pressure background gas of different species.