We a physically-based model of the subsurface of Mars that indicates the Martian conditions should have led to the near-surface subsurface being fully ice-filled in the upper 1000 m. This comes from an exact solution of the governing equations for water vapor transport on Mars. This result agrees with the many deep craters seen on Mars which show ice to well over 30 m depth. That the pores are fully ice-filled in the near surface is significant in that if a well is drilled, and a heat source is inserted, the resulting melt water should stay in the vicinity of the well, and be recoverable for human use.