We consider a simple nonlinear (quartic in the fields) gauge-invariant
modification of classical electrodynamics, which possesses a regularizing
ability sufficient to make the field energy of a point charge finite. The model
is exactly solved in the class of static central-symmetric electric fields.
Collation with quantum electrodynamics (QED) results in the total field energy
about twice the electron mass. The proof of the finiteness of the field energy
is extended to include any polynomial selfinteraction, thereby the one that
stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in
QED in powers of the field strenth