A self-consistent two-dimensional three moment radio-frequency glow discharge model has been developed for methane feed gas using a fluid model to study the charged species dynamics and its effects on deposition in a polyatomic gas discharge. Swarm data as a function of electron energy are provided as input to the model. The discharge is electropositive since positive ion density is more than negative ion density. The importance of two-dimensional modeling has been emphasized by comparing the plasma variables with those of a one-dimensional model. The model predicts both the radial and axial variations of species densities, electron energy and electric field. The off-axis maxima in species densities, typical for two-dimensional discharge, can be observed. The asymmetry of the discharge generates a self dc bias that has been predicted by a trial and error method. The model also calculates the radial variations of species fluxes to the cathode that are important to predict the film deposition.