A global integral model of an arc discharge in helium with sputtered composite metal-graphite anode is presented. The arcing time was measured experimentally for different elements and mass fractions of the metal additions to the graphite anode. The obtained calculated results for pure graphite anode show a good agreement with the experimental and calculated data of other authors. In particular, a good correspondence between the absolute values of electron density and temperature, the discharge voltage and the anode ablation rate as a function of the discharge current was shown. The obtained in the work experimental and calculated data have qualitative agreement, i.e. the anode erosion velocity increases with the addition of Zr, and decreases with the addition of Al.