First results from a two-dimensional (axisymmetric) time-dependent gas dynamic model for the interaction of the solar wind with the local interstellar medium are presented. The model includes the mutual influence of the interstellar and interplanetary plasma (protons and electrons) and the neutral interstellar hydrogen atoms. Neutrals created by charge exchange with the solar wind are ignored; this allows us to approximate the dynamical evolution of the system with the isotropic fluid equations. A supersonic interstellar wind is assumed. The global structure of the heliosphere and interaction region is described for both the plasma and neutral gas. The self-consistent model is compared to a noninteracting gas dynamic model, and dramatic differences in the size of the heliosphere are found. The distribution of neutral hydrogen in the heliosphere is also discussed. ¿ American Geophysical Union 1995