  We have examined some basic properties of damped Ly$\alpha$ systems(DLAs) by
semi-analytic model. We assume that DLA hosts are disk galaxies whose mass
function is generated by Press-Schechter formulism at redshift 3. Star
formation and chemical evolution undergo in the disc. We select modelled DLAs
according to their observational criterion by Monte Carlo simulation using
random line of sights and disk inclinations. The DLA ages are set to be 1 to 3
Gyr. By best-fitting the predicted metallicity distribution to the observed
ones, we get the effective yield for DLAs about $0.25Z_{\odot}$. On the basis
of this constrain, we further compared our model predictions with observations
at redshift 3 in the following items: number density; gas content; HI frequency
distribution; star formation rate density; relationship between metallicity and
HI column density. We found that the predicted number density at redshift 3
agree well with the observed value, but the gas content $\Omega_{DLA}$ is about
3 times larger than observed since our model predicts more DLA systems with
higher column density. The frequency distribution at higher HI column density
is quite consistent with observation while some difference exists at lower HI
end. The predicted star formation rate density contributed by DLAs is
consistent with the most recent observations. Meanwhile, the connection between
DLAs and Lyman Break galaxies(LBGs) is discussed by comparing their UV
luminosity functions which shows that the DLAs host galaxies are much fainter
than LBGs. However, there is a discrepancy between model prediction and
observation in the correlation between metallicity and HI column density for
DLAs. Further investigations are needed for the star formation mode at high
redshift environments.
