  We present a theoretical formalism by which the global and the local mass
functions of dark matter substructures (dark subhalos) can be analytically
estimated. The global subhalo mass function is defined to give the total number
density of dark subhalos in the universe as a function of mass, while the local
subhalo mass function counts only those subhalos included in one individual
host halo. We develop our formalism by modifying the Press-Schechter theory to
incorporate the followings: (i) the internal structure of dark halos; (ii) the
correlations between the halos and the subhalos; (iii) the subhalo mass-loss
effect driven by the tidal forces. We find that the resulting (cumulative)
subhalo mass function is close to a power law with the slope of ~ -1, that the
subhalos contribute approximately 10 % of the total mass, and that the tidal
stripping effect changes the subhalo mass function self-similarly, all
consistent with recent numerical detections.
