  We prove that a Banach space X is not super-reflexive if and only if the
hyperbolic infinite tree embeds metrically into X. We improve one implication
of J.Bourgain's result who gave a metrical characterization of
super-reflexivity in Banach spaces in terms of uniforms embeddings of the
finite trees. A characterization of the linear type for Banach spaces is given
using the embedding of the infinite tree equipped with a suitable metric.
