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It is known that the eigenvalues of the tensor and the tensor-block matrix are invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities of wave propagation of certain media through the eigenvalues of the material tensors. In particular, we consider materials with the anisotropy symbol {1.5} and {5.1}, as well as isotropic materials, and for them we determine the expressions for the velocities of wave propagation. In addition, we obtained expressions for the velocities of wave propagation for materials of cubic syngony with the anisotropy symbol {1,2,3} (the matrix of the elastic modulus tensor components has three independent components), hexagonal system (transversal isotropy) with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has five independent components), trigonal system with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has six independent components), tetragonal system with anisotropy symbol {1,1,1,2,1} (the matrix of the elastic modulus tensor components has six independent components). We also obtained the expressions for the velocities of wave propagation for a micro-polar medium with the anisotropy symbol {1.5.3} and {5.1.3}, and for an isotropic micro-polar material.