In a geometric network G = (S, E), the graph distance between two vertices u, nu is an element of S is the length of the shortest path in G connecting u to nu. The dilation of G is the maximum factor by which the graph distance of a pair of vertices differs from their Euclidean distance. We show that given a set S of n points with integer coordinates in the plane and a rational dilation delta > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most A exists. (c) 2007 Elsevier B.V. All rights reserved.