The dynamics of a walnut tree is investigated in order to better understand the mechanical interaction of trees with wind. Experimental data on the vibrational modes of the tree are obtained, using pull and release tests. These results are then used to validate a previous analytical approach that predicts the organization of modal frequencies as a function of two allometry parameters describing the branched tree geometry. In addition to these experimental results, vibration modes are also obtained from a finite element computation using a detailed digitization of the tree geometry. The comparison between experiments, computation, and the simple analytical approach confirm the specific organization of modes of such branched trees, with a high modal density and a spatial localization. Then the possible biological importance of this organization and the potential biomimetic applications are outlined.