Abstract.If G is a finite connected graph with vertex set V and edge set E, a standard way of defining a distance da on G is to define dG(x, y) to be the number of edges in a shortest path joining x and y in V. If (M, dM) is an arbitrary metric space, then an embedding X: V-> M is said to be isometric if dG(x, y) = dM(\(x), X(y)) for all x, y e V. In this paper we will lay the foundation for a theory of isometric embeddings of graphs into cartesian products of metric spaces.