Tanner Graph representation of linear block codes is widely used by iterative decoding algorithms for recovering data transmitted across a noisy communication channel from errors and erasures introduced by the channel. The stopping distance of a Tanner graph T for a binary linear block code C determines the number of erasures correctable using iterative decoding on the Tanner graph T when data is transmitted across a binary erasure channel using the code C. We show that the problem of finding the stopping distance of a Tanner graph is hard to approximate within any positive constant approximation ratio in polynomial time unless P=NP. It is also shown as a consequence that there can be no approximation algorithm for the problem achieving an approximation ratio of $2^{(\log n)^{1-\epsilon}}$ for any e> 0 unless NP⊆DTIME(npoly(logn)).