In this paper, a two-dimensional continuum fluid model of an rf discharge with suitable boundary conditions is presented. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids, respectively, coupled to Poisson’s equation for the self-consistent electric field. A stable, spatially high-order-accurate, numerical method is presented for solution of this model. Solutions are obtained on an engineering workstation and are shown to be spatially and temporally converged. The resulting solution profiles demonstrate the multidimensional nature of the plasma and illustrate the effects of confining insulating sidewalls and electrode-insulator interfaces.