A model is proposed for the sheath expansion into a nonuniform plasma with substantial drift velocity. We refer in particular to the streaming metal plasma produced by a vacuum are discharge; this kind of plasma is characterized by its spatial nonuniformity and high ion drift velocity. It is shown that for a nonuniform plasma and high substrate bias voltage (>10 kV), the sheath thickness is significantly smaller than in a uniform plasma. High drift velocity also leads to a decrease in sheath thickness. For plasma immersion ion implantation carried out in a nonuniform plasma, the increase in ion implantation current with increasing voltage is different from that of a uniform plasma where the ion current is constant with voltage. This effect was found to be quantitative agreement with experiment. The decrease in sheath thickness with increasing plasma drift velocity can explain qualitatively the experimentally observed existence of a stable high-voltage sheath for a relatively long time.