A nonlinear, analytical model is developed to describe equilibrium Alfv¿n wave structures such as that associated with flow about a conducting obstacle in a flowing plasma. Firstly, in order to give physical insight into the processes involved, we discuss two worked examples one of which extends previous models of the Alfv¿n wave wake produced by the Jovian satellite Io. We describe in detail the fields and, in particular, the current systems associated with the model. Finally, we present a general formalism which leads to a general solution that should be applicable in modeling other incompressible space plasma flows. ¿ American Geophysical Union 1987