We present semi-analytic models and Monte-Carlo simulations of QSO Ly$\alpha$ absorption line systems which originate in gaseous galactic halos, galaxy disks, and satellite halos around central galaxies. The relation between the properties of predicted absorption lines and those of galaxies has been investigated. Using a model with galactic halos, satellites, and HI disks of spirals, 60 % of the observed strong Ly$\alpha$ lines and all of the Lyman-limit systems can be predicted. The models predict $W_r \propto \rho^{-\alpha} L_B^{\beta} (1+z)^{-\gamma}$ with $\alpha \sim 0.5, \beta \sim 0.15, \gamma \sim 0.5$. For strong Ly$\alpha$ lines the average covering factor within $250 h^{-1} \kpc$ is $\sim 0.36$, with an average absorption radius of $\sim 150 h^{-1} \kpc$ for a galaxy halo, in good agreement with observations. Using mock imaging and spectroscopic surveys, selection effects are found to be able to strengthen the anti-correlation between line width and projected distance. The models were also applied to quasar metal absorption lines and more realistic absorption spectra with noise were simulated.