  While the use of galaxy clusters as {\it tools} to probe cosmology is
established, their conventional description still relies on the spherical
and/or isothermal models that were proposed more than 20 years ago. We present,
instead, a deprojection method to extract their intrinsic properties from X-ray
and Sunyaev--Zel'dovich effect observations in order to improve our
understanding of cluster physics. First we develop a theoretical model for the
intra-cluster gas in hydrostatic equilibrium in a triaxial dark matter halo
with a constant axis ratio. In this theoretical model, the gas density profiles
are expressed in terms of the intrinsic properties of the dark matter halos.
Then, we incorporate the projection effect into the gas profiles, and show that
the gas surface brightness profiles are expressed in terms of the
eccentricities and the orientation angles of the dark halos. For the practical
purpose of our theoretical model, we provide several empirical fitting formulae
for the gas density and temperature profiles, and also for the surface
brightness profiles relevant to X-ray and Sunyaev--Zel'dovich effect
observations. Finally, we construct a numerical algorithm to determine the halo
eccentricities and orientation angles using our model, and demonstrate that it
is possible in principle to reconstruct the 3D structures of the dark halos
from the X-ray and/or Sunyaev-Zel'dovich effect cluster data alone without
requiring priors such as weak lensing informations and without relying on such
restrictive assumptions as the halo axial symmetry about the line-of-sight.
