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The present paper is concerned with plane and surface wave solutions of the governing equation for an incompressible, homogeneous, transversely isotropic and rotating thermoelastic medium in the context of the Green–Naghdi theory. The velocity equation for homogeneous plane waves is obtained which indicates the existence of two coupled plane shear waves. The secular equation for Rayleigh waves is derived for thermally insulated as well as isothermal boundaries. The non-dimensional speeds of plane waves are plotted against the angle of incidence, non-dimensional anisotropy parameter and rotation/frequency ratio. The non-dimensional speed of Rayleigh surface waves is also computed against the non-dimensional anisotropy parameter and rotation/frequency ratio.