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The paper analyses the problem of elastic waves propagation through the material reinforced by two families of extensible fibers using high-order shear deformation theories. The material reinforced with two families of fibers can be seen as a material made of an arbitrary number of plies reinforced with one family of fibers, which are at angles ϕ and - ϕ, in relation to the lines of symmetry, so that it can be considered to be a composite laminate. Elasticity constants are derived using strain energy and the theory of invariants. The second-order shear deformation theory was used for creating dynamic equations of motion. Using analytical methods, dispersion curves and diagrams of phase velocities in the polar coordinate system were obtained. The emergence of quasi-modes, in the forms of quasi- bending qA, quasi-extensional qS and quasi-horizontally polarized modes qSH, was shown. The numerical part was done in MATLAB software using combinations of symbolic and numeric values. © 2016, Springer-Verlag Wien.