If a core of dielectric material is coated by a plasmonic structure of
negative dielectric material with non-zero loss parameter, then anomalous
localized resonance may occur as the loss parameter tends to zero and the
source outside the structure can be cloaked. It has been proved that the
cloaking due to anomalous localized resonance (CALR) takes place for structures
of concentric disks and the critical radius inside which the sources are
cloaked has been computed. In this paper, it is proved that CALR takes place
for structures of confocal ellipses and the critical elliptic radii are
computed. The method of this paper uses the spectral analysis of the
Neumann-Poincar\'e type operator associated with two interfaces (the boundaries
of the core and the shell)