The edge effect problem for a flush electrostatic probe is modeled by the flow of a weakly ionized compressible gas past a discontinuous wall potential. The basic flow is a Couette flow and the potential jump is applied at the lower wall which is thus divided into positive and negative current collectors. For a sufficiently small applied potential discontinuity the problem may be linearized about a basic state whose characteristics are known numerically. The linear problem retains the full coupling and ellipticity of the nonlinear one. Results are presented for the total current collected by each electrode, the magnitude of the jump in current density at the junction of the electrodes and the dependence of this quantity on Reynolds number, the first‐order moments of the current density, and the upstream and downstream length scales for the current collection. For conditions investigated here, these length scales are several channel thicknesses. Thus, the operation of a flush electrostatic probe may be completely dominated by edge effects.