The influence of elastic scattering on the resolution of the ballistic electron emission microscope was analyzed with the Monte Carlo modeling method. It was found that the resolution is not reduced even at the lower limit of the mean free path range for this kind of interaction, though the signal-to-noise ratio was decreased. The limiting resolution of about 1 nm is in good agreement with the experiment. Accounting for the escape conditions and the transverse momentum conservation law can make this figure even higher.