A periodic acoustic point source in shallow sea affected by the free surface and the seafloor is analyzed. Sea water is treated as a slightly compressible homogeneous inviscid fluid, and the material of the seafloor is assumed to be poroelastic. The solution of this problem may be represented as an integration of plane wave expansion of the point source, multiplied by the plane reflection coefficients of the boundaries. In this study, an asymptotic solution of this integration obtained by the method of the steepest descent is adapted. A new plane wave reflection coefficient of the seafloor found by the authors of this study and an idealized plane reflection coefficient of the free surface are applied. Pressure amplitude distributions for different frequencies of sound and for different seafloor materials are presented. It is found that the wave attenuation is very slow, hence it is a problem to apply radiation boundary conditions at the outer fields in numerical computation. It is also found that different seafloor materials assumptions give very different solutions of acoustic waves in layered sea water.