We report on our attempt for the first non-LTE modeling of gaseous metal disks around single DAZ white dwarfs recently discovered by Gaensicke et al. and thought to originate from a disrupted asteroid. We assume a Keplerian rotating viscous disk ring composed of calcium and hydrogen and compute the detailed vertical structure and emergent spectrum. We find that the observed infrared CaII emission triplet can be modeled with a hydrogen-deficient gas ring located at R=1.2 R_sun, inside of the tidal disruption radius, with Teff about 6000 K and a low surface mass density of about 0.3 g/cm**2. A disk having this density and reaching from the central white dwarf out to R=1.2 R_sun would have a total mass of 7 10**21 g, corresponding to an asteroid with about 160 km diameter.
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