  The evidence for neutrino masses in atmospheric and solar neutrino
experiments provides further support for the embedding of the Standard Model
fermions in the chiral 16 SO(10) representation. Such an embedding is afforded
by the realistic free fermionic heterotic-string models. In this paper we
advance the study of these string models toward a non-perturbative analysis by
generalizing the work of Donagi, Pantev, Ovrut and Waldram from the case of
G=SU(2n+1) to G=SU(2n) stable holomorphic vector bundles on elliptically
fibered Calabi-Yau manifolds with fundamental group Z2. We demonstrate
existence of G=SU(4) solutions with three generations and SO(10) observable
gauge group over Hirzebruch base surface, whereas we show that certain classes
of del Pezzo base surface do not admit such solutions. The SO(10) symmetry is
broken to SU(5)XU(1) by Wilson line. The overlap with the realistic free
fermionic heterotic-string models is discussed.
