  We report results of quark masses in quenched lattice QCD with the
Kogut-Susskind fermion action, employing the Reguralization Independent scheme
(RI) of Martinelli et al. to non-perturbatively evaluate the renormalization
factor relating the bare quark mass on the lattice to that in the continuum.
Calculations are carried out at \beta=6.0, 6.2, and 6.4, from which we find
$m^{\bar{MS}}_{ud} (2 GeV)= 4.23(29) MeV$ for the average up and down quark
mass and, with the $\phi$ meson mass as input, $m^{\bar{MS}}_{s} (2 GeV)=
129(12) MeV$ for the strange mass in the continuum limit. These values are
about 20% larger than those obtained with the one-loop perturbative
renormalization factor.
