The nature of the several microlensing events observed by the MACHO team towards the Large Magellanic Cloud (LMC) is still a controversial subject. Substellar objects and stars with masses larger than ∼ 1M⊙ have been ruled out as major components of a Massive Astrophysical Halo Object (MACHO) Galactic halo. Stars of near half-solar mass, in particular white dwarfs, appear to be the best candidates to explain the observed microlensing events. On the other hand, observational evidence based on the structure of the debris of the Sagittarius dwarf galaxy suggest that the Galactic halo is non-spherical. We use a tri-axial halo model and advanced Monte Carlo techniques to study the contribution of the halo white dwarf population to the dark matter content of the Galaxy.