A two-dimensional model of quasi-free-electrons is used to compute the electron axial distribution on a carbon nanotube and the energy distribution of the field emitted electrons. The nature of the substrate-nanotube contact is taken into account by varying the boundary condition for the electronic wave function. In qualitative agreement with the experimental results to date, regular patterns of the axial electron density and electron accumulation on the nanotube cap are obtained. The energy distribution of the field emitted electrons shows a multiple peak structure superimposed over a very fine distribution of maxima. Such a multiple peak structure is also qualitatively confirmed in experiments. The behavior of the distribution of the emitted electrons with the extraction voltage and with the operation temperature is investigated. (c) 2006 American Vacuum Society.