This is an announcement for the paper "Metrical characterization of super-reflexivity and linear type of Banach spaces" by Florent Baudier. Abstract: 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. Archive classification: Mathematics Subject Classification: 46B20; 51F99 Remarks: to appear in Archiv der Mathematik The source file(s), , is(are) stored in gzipped form as 0704.1955.gz with size 8kb. The corresponding postcript file has gzipped size 78kb. Submitted from: florent.baudier@univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math@arXiv.org.