Ab initio total energy calculation and molecular dynamics simulation on the process of dopant insertion into carbon nanotubes are carried out on the basis of the all-electron mixed basis approach within the local density approximation. First, an upper bound for the height of the potential barrier which is seen by typical alkali metals (Na and K) going through the center of a hexagonal ring of the nanotube is estimated to be 40 eV for Na and 90 eV for K. Next, such an insertion process is simulated with a suitable kinetic energy of the dopant (70 eV for Na and 150 eV for K). It is observed that the carbon atoms are pushed to open the hexagonal ring wider and the dopant passes through. After encapsulation, the hexagonal ring restores its initial configuration, while the impact shock propagates along the nanotube and gradually decays.