Let $G=(V,E)$ be any undirected graph on $V$ vertices and

$E$ edges. A path $\textbf{P}$ between any two vertices $u,v\in V$ is said to be $t$-approximate shortest path if its length is at most $t$ times the length of the shortest path between $u$ and $v$.

We consider the problem of building a compact data structure for a

given graph $G$ which is capable of answering the following query for

any $u,v,z\in V$ and $t>1$.

\centerline{\em report $t$-approximate shortest path between $u$ and $v$ when vertex $z$ fails}

We present data structures for the single source as well all-pairs versions of this problem. Our data structures guarantee optimal query time. Most impressive feature of our data structures is that their size {\em nearly} match the size of their best static counterparts.