Afterbody flows have been chosen as one of three military application challenges that are studied in the TurMMAC project, a UK-Sweden bi-lateral co-operation. The main issues are drag prediction, jet spreading, and mixing (to reduce IR-signature). A supersonic axisymmetric base flow case was the main target for analysis. This case was computed by three partners using different turbulence models ranging from standard eddy-viscosity models to explicit algebraic Reynolds stress models. The complex flow physics involved was, at least, qualitatively resolved and understood, and the turbulence modelling was found to be a critical issue in successful prediction of the aeronautical performance. The baseline measure of success, prediction of the afterbody drag coefficient within 0.5% of the estimated total drag, was fulfilled. One additional test case studied, more relevant to the parameter regimes of UAVs, was a transonic base flow with a rectangular nozzle exit. The case was computed using explicit algebraic Reynolds stress models. The wall pressure distribution was very accurately predicted but the jet plume development and mixing with the ambient flow was not as accurately predicted. Over all a reasonable prediction of the flow features was obtained.