In this paper, acoustic scattering in shallow and deep inhomogeneous waveguides is analyzed. The full acoustic wave equation that describes the scattered and reflected wave fields, as well as all multipathing within the scatterer and the waveguide, is employed. The explicit finite difference time integration and the k–w transform in the space domain (pseudospectral method) were utilized. Properly chosen boundary conditions enabled the authors to model both shallow and deep oceans. The pseudospectral method was compared with the explicit finite difference technique (see Appendix). The pseudospectral method can be valuable for modeling different underwater wave phenomena: It is characterized by much smaller numerical dispersion than the conventional finite difference method. The results show that in shallow ocean, strong resonance coupling between the underwater scatterer and the waveguide may occur. An important conclusion of this paper is that in a limited aperture experiment when the acoustic reflections are beyond the recording aperture (due to the finite length of the recording cable), the measured data are mainly represented by the primary diffraction arrivals and ‘‘diffraction resonances.’’ In this paper, a detailed discussion will be given on the acoustic scattering in an inhomogeneous waveguide. (For the sake of simplicity, an acoustic scatterer of the rectangular shape was considered.) Different complexities (elastic scatterers, more complicated structures of the index of refraction in the water, etc.) will be compounded in the original model and reported elsewhere.