We have tested current models for the atmospheres (including photosphere and low chromosphere) of late-type stars using the D resonance lines of neutral sodium as a diagnostic. To this end, we have measured the equivalent widths of the D lines for a sample of 39 dwarf and 45 giant late-type stars observed with high spectral resolution. We constructed photospheric models over a grid in effective temperature and surface gravity spanning the spectral types F to M, and luminosity classes V and III of the sample stars. The model photospheres were extended into the chromosphere by assuming a suitable scaling from the Sun, and theoretical Nai D equivalent widths were computed over the grid of models including the deviations from local thermodynamic equilibrium. By taking into account both the experimental errors and the possible variations of stellar parameters (effective temperature, surface gravity, sodium abundance and microturbulence), the comparison between observed and computed equivalent widths allows us to state that the model atmospheres we have used can reproduce the observations for the two luminosity classes and for all the spectral types except for the M-type stars. We have discussed the importance of line blanketing in the spectral analysis of these stars, but at present we cannot conclude that this effect would reduce the discrepancy.