The response of two-electron quantum ring system to the short laser pulses of different shapes in the presence of exteal static electric field is studied. The variation of transition probabilities of the two-electron quatum ring from ground state to excited states with a number of parameters is shown and explained. The energy levels and wavefunctions of the system in the presence of static electric field are found by solving the time-independent Schr ¨odinger equation numerically by finite difference method. The shape of the pulse plays a dominant role on the dynamics.