Numerical models for the development of the discharge in a tokamak are considered. A hybrid model which describes the diffusion and convective processes and also the impurity radiation is used as the basis for a detailed study of the filling-gas ionization stage, the formation of the hot plasma column during the period of total current rise and the energy balance in the quasi-steady-state stage of the discharge. The model shows reasonable agreement with experiment at all stages of the discharge in a tokamak.