In plasma etching and deposition processes, the energy distribution of ions incident onto the substrate strongly affects the surface reactions and the film deposition and etching rates. The magnitude and frequency of the rf-bias power applied to the substrate electrode determines the spatiotemporal variations of the sheath potentials and hence the energy distribution of the ions impinging upon the substrate. A self-consistent dynamic model of the sheath, capable of predicting ion energy distributions impinging on a rf-biased electrode, was developed. The model consists of equations describing the charge transport in the sheath coupled to an equivalent circuit model of the sheath to predict the spatiotemporal charge and potential distributions near the surface. Experimental measurements of the energy distributions of ions impinging on a rf-biased electrostatic chuck have also been made in a high density transformer coupled plasma reactor through Ar and Ne plasmas. The predicted ion energy distributions and sheath profiles are in very good agreement with the experimental measurements.