The electrostatic charging of the rings of Saturn is studied by modeling the charging of a thin dense dust cloud. The model is based on a time-dependent solution of a set of equations which include Boltzmann's and Poisson's equations. Plasma loss and photoelectron production within the cloud are included. Several aspects of the cloud's structure (thickness, average particle size, cross sectional profile, and optical depth) and the ambient plasma (density, temperature, and velocity distribution) can be varied to determine the effect of these quantities on the resulting charge and electric fields. It is found that the electric field is often more complicated in structure and stronger in magnitude within the cloud than at its edges. Thermalization of the plasma within the cloud via collisions with other plasma particles or charged dust, which might reduce the large electric fields found within the cloud, is shown to have a negligible effect becaue of the predominance of plasma absorption. The motion and accretion of micron and submicron dust grains within the cloud can be significantly affected because of the strong electric fields there. ¿ American Geophysical Union 1988