<p>This paper develops a new generalized model for the propagation of Rayleigh-type surface waves in a rotating transversely isotropic thermoelastic medium under the influence of initial stress and dual thermal relaxation times. The governing field equations are formulated within the framework of the Lord–Shulman generalized thermoelasticity theory and are transformed using the Hankel transform technique to derive a new secular determinant equation that governs surface wave propagation. The model simultaneously accounts for rotation, anisotropy, and pre-stress, representing a significant extension of classical thermoelastic formulations. Numerical evaluations illustrate the distinct effects of rotation, initial stress, and relaxation times on phase velocity and attenuation coefficients. The results reveal that increasing rotation and pre-stress reduces the phase velocity, while thermal relaxation parameters modify dispersion behavior. The study offers new insights applicable to seismic wave modeling, rotating machinery stability, and material characterization of anisotropic solids.</p>