The formation process of flame kernels in the ignition process by electric sparks has been investigated by using a numerical simulation, which employs unsteady two-dimensional cylindrical co-ordinate systems. In the simulation, effects of the value of the diameter of spark electrodes and the width of the spark gap on the calculated results are mainly examined. The calculated results show that the hot gas kernel produced by a spark discharge takes an ellipsoidal form at first and then develops into a torus. Under some conditions, there exist two high-temperature regions, namely within the rings of torus and just between the spark electrodes. It is also found that a narrow groove is formed inside the torus. These configurations of the flame kernels agree well with those found by schlieren photographs of the practical flame kernels which are taken by a flash-schlieren photographic technic.