Purpose <p>This study aims to investigate Rayleigh-type surface wave propagation in a composite medium composed of an initially stressed exponentially graded fiber reinforced viscoelastic layer overlying an initially stressed, exponentially graded dry sandy viscoelastic layer with corrugated boundary surfaces.</p> Methods <p>An analytical approach is used to derive a closed-form complex frequency equation governing the behavior of surface waves in the layered structure. The real part of this equation provides the dispersion relation, while the imaginary part determines the damping velocity. Several special cases are also explored to validate the results against classical solutions.</p> Results <p>The derived expressions for the phase and damping velocities show close agreement with known classical results. Graphical analyzes demonstrate the influence of various parameters such as initial stress, fiber reinforcement, exponential classification, bulk and shear viscosities, and the sandy parameter on wave behavior.</p> Conclusion <p>The study reveals that material classification, initial stress, and viscoelastic properties significantly affect Rayleigh-type wave propagation. The results contribute to a better understanding of wave mechanics in complex geophysical media and have potential implications for geotechnical and seismic applications.</p>