Heavy quark masses from finite volume effects

I discuss the results of a new calculation of the charm and bottom quark masses in the quenched approximation and in the continuum limit of lattice QCD. The work has been done by the APE group at the ``Tor Vergata{'' University [1] making use of the step scaling method, previously introduced to deal with two scale problems, that allows to take the continuum limit of the lattice data. We have computed the RGI quark masses and then we have connected the results to the (MS) over bar scheme. The continuum numbers are m(b)(RGI) = 6.73(16) GeV for the b-quark and m(c)(RGI) = 1.681(36) GeV for the c-quark, corresponding respectively to m(b)((MS) over bar)(m(b)((MS) over bar)) = 4.33(10) GeV and m(c)((MS) over bar)(m(c)((MS) over bar)) = 1.319(28) GeV. The latter result, in agreement with current estimates, is for us a check of the method.}