  We consider the self-interaction phenomenon in the framework of the
Bopp-Podolsky electrodynamics. In the present paper, we obtain the
self-interaction potential energy of a charge at rest for the spacetimes with
topological defects of two types: for the axially symmetric spacetime of the
straight cosmic string and the spherically symmetric global monopole spacetime.
It is shown that the behavior of this expression depends essentially on the
angular defect, in spite of the Bopp-Podolsky model parameter, which plays the
role of a scale factor. In contrast with the usual Maxwell electrodynamics, the
self-interaction energy for the Bopp-Podolsky electrodynamics appears to be
finite everywhere and the standard renormalization procedure is not required.
