The effective propagation constants of coherent elastic SH wave in composites with random distributed parallel cylindrical nanoholes in host material are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is applied to obtain the scattering waves from the individual cylindrical nanohole. The multiple scattering effects are taken into consideration by the configuration averaging of random distributed scatterers. The effective velocity and attenuation of coherent SH wave are numerically evaluated. The influence of surface stress is discussed based on the numerical results.