The reason why the difficulty pointed out by Pais arises is analized by the general discussion independent of any approximation for the self-stress of an arbitrary elementary particle interacting with arbitrary fields. To do this, the Pais-Epstein-Sawada's formula is generalized for the system with more intricate interaction. The difficulty due to the process of the vacuum polarization type on account of which the non-vanishing self-stress has been given in also discussed.