It has been proposed by other authors that a stellar wind might provide a pressure support at the inner edge of a planetary nebula to prevent the inward motion of material and to insure the ring-like appearance common to most planetary nebulae. The interaction of a supersonic stellar wind with a planetary nebula is examined with three models. In the shock-relation model the shock relations are generalized to allow for arbitrary changes in the mass, momentum and energy flux of the stellar wind. It is found that there exists a restrictive lower limit on the amount of energy that can be removed from a supersonic flow and still satisfy the shock relations. It is concluded that a supersonic stellar wind can not flow into a planetary and cool to observed planetary temperatures (~ 10 °K) and that a shock front must exist between the central star and planetary to reduce the flow to subsonic velocities before reaching the planetary. In the radiation model the subsonic stellar wind is allowed to lose energy by radiation only. It is concluded that the stellar wind does not significantly cool in a distance the order of a planetary radius (~ 104 A.U.), and that in order for the flow to be cooled and slowed to observed planetary expansion velocities (10-30 km/sec), the flow must first transfer energy and momentum to the planetary. In the third model the flow is allowed to transfer energy in coulomb collisions and momentum through a viscous force term to a stationary planetary that is heated by ionization-recombination processes and cooled by radiating in the N1 and N2 forbidden lines of OIII. The distances involved in the solutions are less than the mean free path of the flow particles. It is concluded that processes other than those dominant in the main body of the planetary may need to be taken into account in the region of interaction and that the assumption that fluid dynamics may be applied to this flow problem may not be valid.