The Edge-tenacity Te(G) of a graph G was de ned as Te(G) = min F E(G) f j F j + (G F)! (G F) g where the minimum is taken over all Edge cutset F of G. We de ne G-F to be the graph induced by the Edges of E(G) F, (G F) is the number of Edges in the largest component of the graph induced by G-F and! (G F) is the number of components of G F. A set F E(G) is said to be a Te-set of G if Te(G) = jFj+ (G F)! (G F) Each component has at least one Edge. In this paper we introduce a new invariant Edge-tenacity, for graphs. it is another vulnerability measure. we present several properties and bounds on the Edge-tenacity. we also compute the Edge-tenacity of some classes of graphs.