An implementation of the Ehrenfest method with damped velocity is discussed. The method is then applied to study the non-adiabatic reaction paths for two simple chemical systems: the isomerization of the allene radical cation in its excited state and the channel 3 photochemical transformation of benzene to benzvalene. For both systems the initial conditions for the Ehrenfest trajectory were either an adiabatic eigenstate with the geometry close to a conical intersection, or a superposition of eigenstates at the geometry close to a conical intersection. In allene we were able to show that the adiabatic reaction, which passes through a conical intersection, stimulates electron dynamics. In benzene we were able to show the importance of the phase at the conical intersection for the generation of the benzevalene intermediate.