We present a two-dimensional (2D) plasma model for a coaxial microwave discharge. The microwave energy at driving frequency of 2.45 GHz is fed into a coaxial configuration in which the plasma acts as an outer conductor in such a way that a spatially extended surface wave is created. This geometry permits large surface treatment, especially if a set of such coaxial lines are used. The 2D model describes the plasma as a two-temperature non-chemical equilibrium fluid sustained by electromagnetic surface waves. We present results for argon as a working gas. The importance of wave–plasma power coupling and electron heat transport is discussed. The radial localization of electron density in the coaxial plasma waveguide is observed and compared with experimental results. Moreover, a parameter study allows one to investigate the dependence of radial contraction of the electron density as a function of pressure in the range 2–8 mbar, and also the dependence of electron density with power input in the range 120–1200 W. In order to verify the model, the modelling results are compared with experimental results for the electron density and temperature and good agreement is found.