Abstract. The vertex (resp. edge) metric dimension dim(G) (resp. edim(G)) is the minimum number of vertices of G which distinguish all pairs of vertices (resp. edges) in G by means of distance. Typically, dim(G)\le edim(G). For every a and b, such that 4\le b < a, we construct a 2-connected graph G with dim(G)=a and edim(G)=b.