The paper presents results of research some physical and computational features of unloaded power transmission lines switching-offs. It was stated that there are not monotonous dependence between magnitudes of transitional voltages at switching-off high voltage aerial lines and their lengths. There was studied influence of the circuit-breaker type (SF6 or vacuum ones) on transitional voltages. Features of use the ordinary differential equations' solvers at computer simulation from the point of view stability of solutions and simulation time consuming were investigated in the presented research.