A high statistics lattice calculation of quark masses with a non-perturbative renormalization procedure.

We present results of a high statistics study (O(2000) configurations) of the quark masses in the <(MS)over bar> scheme from Lattice QCD in the quenched approximation at beta = 6.0, beta = 6.2 and beta = 6.4 using both the Wilson and the tree-level improved SW-Clover fermion action. We extract quark masses from the meson spectroscopy and from the axial Ward Identity using non-perturbative values of the renormalization constants. We compare the results obtained with the two methods and we study the O(a) dependence of the quark masses for both actions. Our best results are m(s)(<(MS)over bar>)(2 GeV) = (123+/-4+/-15) MeV and m(c)(<(MS)over bar>)(2 GeV) = (1525+/-40+/-100) MeV.