Using a relatively simple three-dimensional model for a stratified plasma cloud surrounded by uniform ambient plasma, configurations of the density profile within the cloud are determined which permit uniform E¿B motion of the cloud. The applied current density field which drives induced electrostatic potentials is permitted to have variation along the direction of the magnetic field and finite parallel resistivity is explicitly considered. The analysis and calculations suggest that exact uniform motion of the plasma cloud requires the plasma density within the cloud be smallest where the neutral wind is largest. Conversely, the plasma density is largest where the neutral wind is smallest. Quantitative examples suggest that the uniform motion of a long high-density plasma cloud across the magnetic field is most likely to occur if the neutral wind has a component which is relatively uniform along the length of the plasma cloud. Qualitative application of the analytical and quantitative results is made to an assemblage of striations which are assumed to be a set of planar plasma sheets.