We have studied the interaction of fast solar wind hydrogen atoms with the martian atmosphere by a three-dimensional Monte Carlo simulation. These energetic neutral hydrogen atoms, H-ENAs, are formed upstream of the martian bow shock. Both H-ENAs scattered and non-scattered from the martian atmosphere/exosphere were studied. The colliding H-ENAs were found to scatter both to the dayside and nightside. On the dayside they contribute to the so-called H-ENA albedo. On the nightside the heated and scattered hydrogen atoms were found also in the martian wake. The density, the energy distribution function and the direction of the velocity of H-ENAs on the nightside are presented. The present study describes a novel "ENA sounding" technique in which energetic neutral atoms are used to derive information of the properties of planetary exosphere and atmosphere in a similar manner as the solar wind photons are used to derive atmospheric densities by measuring the scattered UV light. A detailed study of the direction and energy of the scattered and non-scattered H-ENAs suggest that the ENA sounding is a method to study the interaction between the planetary atmosphere and the solar wind and to monitor the density, and likely also the magnetization, of the planetary upper atmosphere. Already present-day ENA instrument should be capable to detect the analyzed particle fluxes.