A model of sequential ͑incoherent͒ tunneling for the electron field emission was built up in order to explain some peculiarities of the electronic emission from relatively thick dielectric layers covering nanometer-range tips, particularly carbon nanotubes. The emission current as a function of applied voltage, dielectric layer thickness, polarizability, and temperature was computed. Various experimentally detected trends were thereby modeled, leading to the conclusion that incoherent tunneling might be a competitive mechanism for electron field emission from dielectric layers on the tips of nanometer-sized cathodes.