Recent multidimensional numerical simulations [Pauls et al., 1995> of the solar wind interaction with the local interstellar medium have produced a self-consistent description of the interstellar neutral hydrogen at the heliopause. In this report, we develop a simple one-dimensional model of the solar wind interaction with interstellar hydrogen which is capable of describing the basic features of the interaction along the solar wind stagnation line that were obtained in the numerical simulations. It is shown that pickup ions in the subsonic solar wind can stagnate the plasma flow completely at a distance of 40 AU from the termination shock thus defining the position of the contact discontinuity relative to the termination shock. The plasma number density increases considerably but remains finite on the solar wind side of the contact discontinuity, for a finite velocity of the neutral hydrogen. For the interstellar wind, deceleration due to the interaction with solar hydrogen is found to be important, even though the solar hydrogen density flux is relatively small. The characteristic scale of this interaction is defined by the depth of penetration of the solar hydrogen atoms into the interstellar wind. We find that for observed solar wind and interstellar medium parameters, the deceleration is sufficient to stagnate the interstellar wind at the contact discontinuity. ¿ 1996 American Geophysical Union