We investigate Damped Ly-alpha absorbing galaxies (DLA galaxies) at low redshifts z<1 in the hierarchical structure formation scenario to clarify the nature of DLA galaxies because observational data of such galaxies mainly at low redshifts are currently available. We find that our model well reproduces distributions of fundamental properties of DLA galaxies such as luminosities, column densities, impact parameters obtained by optical and near-infrared imagings. Our results suggest that DLA systems primarily consist of low luminosity galaxies with small impact parameters (typical radius about 3 kpc, surface brightness from 22 to 27 mag arcsec^{-2}) similar to low surface brightness (LSB) galaxies. In addition, we investigate selection biases arising from the faintness and from the masking effect which prevents us from identifying a DLA galaxy hidden or contaminated by a point spread function of a background quasar. We find that the latter affects the distributions of DLA properties more seriously rather than the former, and that the observational data are well reproduced only when taking into account the masking effect. The missing rate of DLA galaxies by the masking effect attains 60-90 % in the sample at redshift 0<z<1 when an angular size limit is as small as 1 arcsec. Furthermore we find a tight correlation between HI mass and cross section of DLA galaxies, and also find that HI-rich galaxies with M(HI) sim 10^{9} M_sun dominate DLA systems. These features are entirely consistent with those from the Arecibo Dual-Beam Survey which is a blind 21 cm survey. Finally we discuss star formation rates, and find that they are typically about 10^{-2} M_sun yr^{-1} as low as those in LSB galaxies.
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