The modelling of a gliding arc discharge (GAD) is studied by means of the quasineutral (QN) plasma modelling approach. The model is first evaluated for reliability and proper description of a gliding arc discharge at atmospheric pressure, by comparing with a more elaborate non‐quasineutral (NQN) plasma model in two different geometries – a 2D axisymmetric and a Cartesian geometry. The NQN model is considered as a reference, since it provides a continuous self‐consistent plasma description, including the near electrode regions. In general, the results of the QN model agree very well with those obtained from the NQN model. The small differences between both models are attributed to the approximations in the derivation of the QN model. The use of the QN model provides a substantial reduction of the computation time compared to the NQN model, which is crucial for the development of more complex models in three dimensions or with complicated chemistries. The latter is illustrated for (i) a reverse vortex flow (RVF) GAD in argon, and (ii) a GAD in CO2. The RVF discharge is modelled in three dimensions and the effect of the turbulent heat transport on the plasma and gas characteristics is discussed. The GAD model in CO2 is in a 1D geometry with axial symmetry and provides results for the time evolution of the electron, gas and vibrational temperature of CO2, as well as for the molar fractions of the different species.