A 2-D axisymmetric model of a microwave plasma ball reactor, as used in plasma assisted chemical vapor deposition systems, has been developed. The model can be broken down into two main parts. Firstly, a model of the microwave coupling to the discharge and secondly, a collision-radiative-diffusion model of the discharge plasma. Self-consistent solutions are obtained incorporating these two components of the model. The model is able to compute the position, size, and shape of the plasma ball in the reactor in addition to the general discharge properties such as 2-D excited state density, electron density, and electron temperature profiles. In addition to describing the key features of the model, results are presented from initial calculations performed for a hydrogen discharge plasma. These results are compared to experimental measurements to show the predictive capabilities of the model. Also discussed are the latest improvements in the model, which allow it to deal with admixtures of methane and hydrogen. Particular emphasis is put on the key species for diamond deposition and how their concentrations vary with reactor conditions. The model represents a valuable tool for the optimization of diamond deposition systems, and as such, further extensions to the model to improve its predictive capabilities are discussed.