Two-dimensional magnetohydrodynamic simulations of the solar wind interaction with the magnetized regions on the surface of the Moon suggest mini-magnetospheres can form around the regions on the Moon when the magnetic anomaly field strength is above 10 nT at 100 km above the surface (for a surface field strength of 290 nT) and when the solar wind ion density is below 40 cm-3, with typical observations placing anomalous magnetic field strengths around 2 nT at 100 km above the surface. The results suggest that not only can a bow shock and magnetopause form around the small anomalies, but their position and shape can change dramatically with changes in the solar wind conditions. A switch from southward to northward interplanetary magnetic field (IMF) causes the size of the mini-magnetosphere to increase by 90% and the magnetic field at various positions inside the bow shock to increase by a factor of 10. In addition to affecting the stand-off distance, changes in the IMF can also cause the mini-magnetosphere to go from very round to flat and elongated. The scale size of the mini-magnetospheres is 100 km for the range of typical solar wind conditions and the surface magnetic field strengths measured by Lunar Prospector. A stagnation point inside the shock region also exists for several solar wind conditions. ¿ 2000 American Geophysical Union