  Shape measurements of galaxies and galaxy clusters are widespread in the
analysis of cosmological simulations. But the limitations of those measurements
have been poorly investigated. In this paper, we explain why the quality of the
shape measurement does not only depend on the numerical resolution, but also on
the density gradient. In particular, this can limit the quality of measurements
in the central regions of haloes. We propose a criterion to estimate the
sensitivity of the measured shapes based on the density gradient of the halo
and to apply it to cosmological simulations of collisionless and
self-interacting dark matter. By this, we demonstrate where reliable
measurements of the halo shape are possible and how cored density profiles
limit their applicability.
