We study the structural robustness of metabolic networks on the basis of the concept of elementary flux modes. It is shown that the number of elementary modes itself is not an appropriate measure of structural robustness. Instead, we introduce three new robustness measures. These are based on the relative number of elementary modes remaining after the knockout of enzymes. We discuss the relevance of these measures with the help of simple examples, as well as with larger, realistic metabolic networks. Thereby we demonstrate quantitatively that the metabolism of Escherichia coli, which must be able to adapt to varying conditions, is more robust than the metabolism of the human erythrocyte, which lives under much more homeostatic conditions.