This paper describes the investigation of low pressure supersonic plasma jets as found in LPPS processes. The main objective is to develop and validate a two-dimensional axisymmetric mathematical model representing such flows. Due to the supersonic nature of the jet, insertion of a measurement probe leads to the appearance of a detached shock in front of the probe. Consequently plasma values are measured behind the probe-induced shock, namely the stagnation enthalpy (ho), the stagnation pressure (po) and the static pressure (p). The first two values are taken from enthalpy probe measurements while the third value comes from a new technique. Combining these measurements, a new interpretation method enables the calculation of the free-stream supersonic plasma jet properties. The mathematical model is validated using the enthalpy probe measurements and the free-stream properties from the new interpretation method. Results show that the model does not predict a static pressure as large as the new interpretation method. The principal cause for this discrepancy is attributed to the LTE assumption which is questionable for a 40 mbar plasma jet. The modelling effort reported here confirms the need to develop more detailed mathematical models for low pressure supersonic plasma jets in the future.