In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two di erent vulnerability parameters of graphs, Tenacity and rupture degree are de ned. In general, computing the Tenacity of a graph is NP-hard and the rupture degree of a graph is NP-complete, but in this paper, we will show that these parameters can be computed in polynomial time for interval graphs.