Abstract: Assuming that shallow water with a positive sound velocity gradient has a rough surface,the change of surface height is a stationary stochastic process with Gaussian distribution.The normal-modes which can reach receiver are summed according to energy,and an expression for the averaged intensity is then obtained by averaging over the source and receiver depth witthin the turning-depth of pseudo-plane waves corresponding to these normal-modes.Theoretical results are in good agreement with experimental data.The structure of the sound field in the case of a quiet sea surface as a special case of rough surface.