A model of near-cathode layers in vacuum arcs is developed. The model relies on a numerical solution of the problem of near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface1 and allows one to self-consistently determine all parameters of the near-cathode layer, including the ion backflow coefficient, as functions of the local surface temperature Tw and the near-cathode voltage U. Evaluation results are given for Cu and CuCr cathodes. The dependence of the density of energy flux from the plasma to the cathode surface on Tw for fixed U is shown to be non-monotonic with a maximum. This feature stems from the fact that the ion heating of the cathode grows faster than the electron emission cooling at lower Tw and vice versa at higher Tw. This feature is very important theoretically and suggests that spots on cathodes of vacuum arcs may appear due to thermal instability developing in the cathode body and that stationary regimes of cathode spots in vacuum arcs are possible, similarly to what happens in the theory of cathode spots in high-pressure arc discharges.