Dusty plasmas are present in comets, in the ring systems of the outer planets, and in the interstellar medium. A two-dimensional particle-in-cell (PIC) model of a dusty plasma is presented in this paper. The PIC code is best suited for modeling the plasma-dust interaction for large grains, with diameters of the order of a centimeter. We have modeled the charging process for an individual dust grain and the associated potential pattern in the surrounding plasma. We have also considered the case of a large number of grains in a plasma, with intergrain separations of the order of the Debye length, and have shown that the plasma becomes depleted and the charge on a dust grain is reduced, as other workers in this field have predicted (cf. C. K. Goertz, 1989). We examine the electron and ion distribution functions in the vicinity of a charged grain and demonstrate that the ions near a grain have clearly been accelerated by the electrostatic potential. ¿ American Geophysical Union 1994