  We present a detailed non-spherical modeling of dark matter halos on the
basis of a combined analysis of the high-resolution halo simulations (12 halos
with $N\sim 10^6$ particles within their virial radius) and the large
cosmological simulations (5 realizations with $N=512^3$ particles in a
$100h^{-1}$Mpc boxsize). The density profiles of those simulated halos are well
approximated by a sequence of the concentric triaxial distribution with their
axis directions being fairly aligned. We characterize the triaxial model
quantitatively by generalizing the universal density profile which has
previously been discussed only in the framework of the spherical model. We
obtain a series of practically useful fitting formulae in applying the triaxial
model; the mass and redshift dependence of the axis ratio, the mean of the
concentration parameter, and the probability distribution functions of the the
axis ratio and the concentration parameter. These accurate fitting formulae
form a complete description of the triaxial density profiles of halos in Cold
Dark Matter models. Our current description of the dark halos will be
particularly useful in predicting a variety of nonsphericity effects, to a
reasonably reliable degree, including the weak and strong lens statistics, the
orbital evolution of galactic satellites and triaxiality of galactic halos, and
the non-linear clustering of dark matter. In addition, this provides a useful
framework for the non-spherical modeling of the intra-cluster gas, which is
crucial in discussing the gas and temperature profiles of X-ray clusters and
the Hubble constant estimated via the Sunyaev -- Zel'dovich effect.
