  Cloaks for underwater applications designed for actual submarine acoustic
stealth are still far from the technological advancement needed for being put
in practice. Several challenges are to be overcame such as dealing with weight
or non-axisymmetric shapes. In this paper, we introduce the use of elliptical
coordinates to define quasi-symmetric transformations to retrieve the material
properties of pentamode cloaks for elliptical shaped targets, along with a
quantifiable approximation introduced by the rotation tensor being different
from the identity. This is done analitically adopting transformation theory, in
an attempt to generalize the usual approach for axisymmetric cloaks, with the
aim of dealing with shapes closer to those of the actual cross section of a
submarine. With respect to existing techniques for dealing with arbitrarily
shaped pentamode cloaks, the introduced technique allows for a priori control
on the principal directions of anisotropy and for enlarged design space in
terms of possible combinations of material property distributions for the same
geometry of the problem.
