The coherent component of sound propagating in a shallow water acoustic environment suffers attenuation with range due to the irreversible scattering of energy into the incoherent component by a rough ocean surface. Using a ’’frozen surface’’ approximation, the relevant description of the surface roughness for this problem is the Fourier transform of the spatial autocorrelation of the surface, which is the symmetric part of the wave spectra reported in the literature. The attenuation coefficients of the normal modes are calculated using a boundary perturbation method, and the directional dependence of these are deduced analytically from the anisotropy of the surface wave spectrum. An anisotropy of the form cos2φ gives a directional dependence of the forman+bncos2ϑ for thenthnormal mode. The parametersanandbnare calculated from the radial portion of the spectrum, and from the eigenfunction and eigenvalue of the normal mode. The direction of propagation ϑ of the acoustic wave is measured from the wind direction. Calculations are performed for a Pekeris model of the ocean acoustic environment.