The normal mode solution of the problem of the radiation field of a simple harmonic point source in a layered wave guide is extended to the case of a band‐limited noise source. This theory is used to calculate the radiation field of a simple harmonic point source and a point noise source in shallow water over a thick layer of unconsolidated sediments, and the calculations are compared with experimental data. The experimental dependence of the acoustical pressure upon source distance is in agreement with that calculated from the theory.