Abstract <p>The study of disturbance propagating as waves across a transversely isotropic medium is the focus of this article. In addition to macroscopic translational deformation, the particles in the considered medium also exhibit small-scale internal rotation. The medium is micropolar by nature as a result of this additional translational flexibility. In addition, the medium is incompressible, and given particular plan-strain conditions, the dispersion relation of waves propagating through the media is obtained. We may infer from the dispersion relation that three transverse waves propagate across the medium due to incompressibility. Non free boundary conditions are employed to find out the reflection coefficients. Effect of different values of nonlocal parameter is studied. For a certain media, the findings are visually displayed. The suggested model is used to simulate the mechanical properties of complex materials, such biological tissues and composites that include microstructural heterogeneity. A comparison is made with the results obtained by others when the external parameters neglected that indicate to the strong impact for the new parameters. The results applicable to a variety of domains, including acoustics, engineering, geophysics, and astronomy.</p>