A two-flux radiation model of the helical instability of arcs in axial magnetic field is presented. The temperature (and electrical conductivity) is approximated in a more realistic way (parabolic instead of flat profile) and a simplified term of radiation losses is included in the energy equation. The magnetohydrodynamic equations in an electrostatic approximation serve as the starting point of the theory. Using a linear time-dependent perturbation theory, the corresponding equations and an explicit analytic expression that corresponds to the term of radiation losses are derived in the presence of the radiation transfer energy, from which the marginal Maecker number and the growth rate of the helical instability can be given. It is found that, in comparison with the results without radiation, the arc stable area is reduced.