The “Galaxy Model” (GalMod) is a theoretical population synthesis model able to simulate synthetic surveys of the Milky Way, M31, and able to generate initial conditions for quasi-equilibrium collisionless models. GalMod assumes the Galaxy to be a discrete superposition of several composite stellar populations (CSPs) representing a few nominal significant stellar populations: the thin disk, the thick disk, the stellar halo, and the bulge. GalMod immerses these CSPs in a single dark matter (DM) halo component and a hot coronal gas component (HCG). A parametric model for the modeled galaxy gravitational potential is computed to secure consistency with the density profiles by solving the Poisson equation. These density profiles generate synthetic Hertzsprung-Russell and color-magnitude diagrams (CMDs) in several photometric bands, including updated Gaia DR2 photometry and Subaru Hyper Suprime-Cam. Finally, the gravitational potential is used to realize the stellar kinematics. A global model for the Milky Way’s gravitational potential is built to secure consistency with the density profiles by solving the Poisson equation. In turn, these density profiles are used to generate synthetic probability distribution functions (PDFs) for the allocation of stars in the CMDs. Finally, the gravitational potential is used to constrain the stellar kinematics using the moment method on phase-space distribution functions. GalMod contains non-axisymmetric Galactic components such as the spiral arms, bar, and photometric extinction. The realization of the f.o.v. has no size limit; even full-sky synthetic surveys are possible.