A multi-string model is given for the computer simulation of radiation characteristics (spectral and angular densities, radiation energy losses) for axial electron channeling in crystals. The spectral and angular distributions of the radiation in the channeling and above-barrier motion regimes are obtained by simulation of the trajectories of axially channeled electrons. Besides, the simulated data on the passage of electrons through axial channels of single crystals are presented. The results are compared with experiments.