Neutrino oscillations inside matter are very sensitive to the density of the medium traversed by the neutrinos. If the neutrino mixing angle (so far unknown) is not very small, then the neutrino oscillation length is of the size of the Earth, and we can use the phenomenon of neutrino matter oscillations to study the Earth's density distribution. Although neutrino attenuation data have already been proposed as a means to infer the density structure of the Earth, we show that neutrino oscillation data could also be used to make a density tomogrpah of the Earth. A numerical experiment in which neutrino beams from an accelerator are sent across the Earth, and are detected at six different locations on the Earth's surface, shows the feasibility of using neutrino oscillation data, with the advantage of using only currently available neutrino energies. ¿ American Geophysical Union 1991