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We present a semi-analytic model of satellite galaxies, SatGen, which cangenerate large samples of satellite populations for a host halo of desiredmass, redshift, and assembly history. The model combines dark-matter halomerger trees, empirical relations for the galaxy-halo connection, and analyticprescriptions for tidal effects, dynamical friction, and ram pressurestripping. SatGen emulates cosmological zoom-in hydro-simulations in certainaspects. Satellites can reside in cored or cuspy DM subhaloes, depending on thehalo response to baryonic physics that can be formulated from hydro-simulationsand physical modeling. The subhalo profile and the stellar mass and size of asatellite evolves depending on its tidal mass loss and initial structure. Thehost galaxy can include a baryonic disc and a stellar bulge, each described bya density profile that allows analytic orbit integration. SatGen complementssimulations by propagating the effect of halo response found in simulated fieldgalaxies to satellites (not properly resolved in simulations) and outperformssimulations by sampling the halo-to-halo variance of satellite statistics andovercoming artificial disruption due to insufficient resolution. As a firstapplication, we use the model to study satellites of Milky Way sized hosts,making it emulate simulations of bursty star formation and of smooth starformation, respectively, and to experiment with a disc potential in the hosthalo. Our model reproduces the observed satellite statistics reasonably well.Different physical recipes make a difference in satellite abundance and spatialdistribution at the 25% level, not large enough to be distinguished by currentobservations given the halo-to-halo variance. The MW disc depletes satellitesby 20% and has a subtle effect of diversifying the internal structure ofsatellites, important for alleviating certain small-scale problems.

SatGen: a semi-analytical satellite galaxy generator -- I. The model and its application to Local-Group satellite statistics