In this research, we presented a study of the stability of flow systems and heat transfer in horizontal channels under the influence of the vertical magnetic field as well as thermal radiation where we built a mathematical model and put the partial differential equations that control the model and we analyze these equations after transformation into non-dimensional equations into two parts: the first unsteady state equations and second steady state equations, hence analyze the stability on the unsteady state equations. It’s noticed that the increase of Reynolds number Re causes the increase to unstable probability of the system. But the increase of Schmidt number has an effect on the system towards unstable, as well as the increase of grash of number makes the system stable. Finally, the increase of wave number k has a positive effect towards stable.