  We present a model for the disk of the classical Be star $\zeta$ Tauri. The
model consists of a Keplerian rotating disk with a power-law surface density
and a vertical density distribution that follows from the balance between the
thermal gas pressure and the z-component of the stellar gravitation. The
opening angle of such a disk is not a fixed value but increases with the
distance to the star (flared disk). We use a Monte Carlo code that solves
simultaneously the thermal equilibrium, the statistical equilibrium and the
hydrostatic equilibrium equations. The result is a self-consistent solution for
the electron temperature, level populations and gas density distribution. It
follows from this model that the only free parameter is the disk density. All
other parameters (e.g. shape of the disk surface) are self-consistently
calculated given the disk density. In this paper we present a successful fit
for $\zeta$ Tauri data using this model.
