Abstract: Two-dimentional ideal MHD simulation of the interaction between the solar wind and the Moon reveals the particle and magnetic field distribution in the lunar wake. The results show that the density of the solar wind falls ramatically and the interplanetary magnetic field increases in the umbra of the Moon. When the interplanetary magnetic field is parallel to the direction of the solar wind velocity, the wake is very long. When the magnetic field is normal to the velocity of the solar wind, the wake is shorter.