  We study the influence of structural obstacles in a disordered environment on
the size and shape characteristics of long flexible polymer macromolecules. We
use the model of self-avoiding random walks on diluted regular lattices at the
percolation threshold in space dimensions d=2, 3. Applying the Pruned-Enriched
Rosenbluth Method (PERM), we numerically estimate rotationally invariant
universal quantities such as the averaged asphericity A_d and prolateness S of
polymer chain configurations. Our results quantitatively reveal the extent of
anisotropy of macromolecules due to the presence of structural defects.
