The outflowing solar wind interacts with the local interstellar medium to form the heliospheric cavity within which the solar wind is supersonic. Because the interstellar medium is moving with respect to the Sun, and because the solar wind has a latitude dependence, the heliosphere is asymmetric. The flow of the interstellar medium past the heliosphere produces an asymmetry because of the Bernoulli effect, which draws the heliosphere out in a direction orthogonal to the upstream-downstream axis, and because of a viscous interaction, which draws out the heliosphere downstream. We consider a variety of cases and find the effects to be significant with, typically, the upstream direction having a heliospheric dimension that is 2/3 the downstream dimension. Suggestions have been put forth to the effect that a spacecraft penetration of the heliospheric shock wave may be imminent. Because one of the most distant spacecraft is moving roughly in the upstream direction relative to the interstellar flow, and the other is moving in the downstream direction, the distance to their encounters with the heliospheric shock may differ by as much as 40 AU. ¿ American Geophyscial Union 1987