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 Letter, 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.