Surface roughness influences significantly the quality factor of high frequency nanoresonators for large frequency - relaxation times within the non-Newtonian regime, where a purely elastic dynamics develops. It is shown that the influence of sort wavelength roughness, which is expressed by the roughness exponent H for the case of self-affine roughness, plays significant role in comparison with the effect of the long wavelength roughness parameters such as the rms roughness amplitude and the lat...