Plasma source ion implantation utilizes negative high voltage pulses applied to targets immersed in a plasma. This produces an expanding shea which accelerates ions into the target. A model for expanding sheaths at dielectric surfaces is developed; the significant differences between this and metal targets are the finite dielectric constant of the material and accumulation of charge in the nonconducting material. A model is developed for an expanding sheath at a dielectric surface and applied to a polyethylene sheet as an example. The most significant effect is the reduction of the energy at which ions are implanted in the material because of charging at the surface of the polyethylene.