Abstract： A mathematical model and analysis methods for the internal waves generated by pulsating point sources were theoretically established, and the analytic expression of the free-surface Green’s function for ω2>N2 in uniformly density-stratified fluids was derived based on the Fourier transformation and contour integration technique, where N is the buoyancy (or Brunt-V-is-l) frequency. Compared with the previous Green’s function of internal waves, this paper laid emphasis on the consideration of the free surface. A complete description of the properties of solution and the free-surface fluctuation characteristics were discussed in detail. In fact, the pulsating sources do not produce the real internal waves when ω2>N2. The analytical solution corresponds to the influence of density uniformly stratified upon the commonly used Green’s function, which is extremely intuitive on the radiation term.