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Tumors with anisotropy in their structural properties experience unpredictable and asymmetric growth along certain directions that can vary over time during the tumor progression. An early recognition of such anisotropy could provide information about their malignity, facilitating early diagnostics/prognostic. However, it is difficult to be observed by classic echography. Diverse studies of the literature show 3D images of elastic properties in media with anisotropy in a certain direction, but are transversely isotropic. However, for highly anisotropy media this assumption is no longer valid and requires specific measurements of shear velocities in the 3D directions. These media with 21 independent elastic material parameters and no symmetry plane. Techniques using ultrafast focused sound scanners present difficulties in covering immediate regions around the focused area and specific information for different incident beam orientations to obtain complete 3D spatial information, which is relevant in these types of media without planes of symmetry. It is the case of malignant tumors. The current paper presents a flexible spatial study of mechanical displacements induced in highly anisotropic soft media by low frequency shaker (including printed inorganic, pseudo-organic grids and cow fiber tissues respectively). Homogeneous and heterogeneous media without planes of symmetry have been tested in the experiments by using speckle ultrasonic interferometry. Velocities associated to the induced low frequency-mechanical displacements have been analyzed at a point of interest within the sample from different angles of propagation, covering a 3D angular space. These measurements show a high spatial-dependence of results, demonstrating the relevance of making spatial angular scans to derive parameters related to the anisotropy. This technique allows detection of anisotropies in small areas of analysis, even if they are weak, AEI/FEDER, UE DPI2017-90147-R