An extensive collisional-radiative model for the argon atoms in a glow discharge has been developed. Sixty-five effective argon atomic levels are considered. The processes taken into account are radiative decay, electron, fast argon ion and argon atom and thermal argon atom impact ionization, excitation and deexcitation between all the levels, electron-ion radiative recombination, and electron-ion three-body recombination where the third body is an electron, fast argon ion or atom, or a thermal argon atom. Some additional processes are incorporated for the two $\text{4s}$ metastable levels, i.e., Penning ionization of sputtered atoms, two- and three-body collisions with argon ground state atoms, collisions between two atoms in a metastable level, and diffusion and subsequent deexcitation at the walls. Typical results of the model are the populations of the various excited levels as a function of distance, and the relative contributions of different populating and depopulating processes for all levels.