  The calculation of Yukawa couplings in F-theory GUTs is developed. The method
is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion
masses based on family symmetries coming from the SU(5)_\perp factor in the
underlying E(8) theory. The remaining Yukawa couplings involving the light
quark generations are determined by the Froggatt Nielsen non-renormalisable
terms generated by heavy messenger states. We extend the calculation of Yukawa
couplings to include massive states and estimate the full up and down quark
mass matrices in the SU(5) model. We discuss the new features of the resulting
structure compared to what is usually assumed for Abelian family symmetry
models and show how the model can give a realistic quark mass matrix structure.
We extend the analysis to the neutrino sector masses and mixing where we find
that tri-bi-maximal mixing is readily accommodated. Finally we discuss
mechanisms for splitting the degeneracy between the charged leptons and the
down quarks and the doublet triplet splitting in the Higgs sector.
