For accurate measurement of acoustic properties using an impedance tube, the generated acoustic wave must propagate within the waveguide as a plane wave. In impedance tube standards, the dimensions of the waveguide are selected such that plane-wave propagation is ensured. Owing to the absence of a standard for impedance tubes operating in water and the closer acoustic impedance matching between water and the waveguide walls compared with air, it is necessary to investigate plane-wave propagation in water-filled waveguides. In this study, wave propagation inside a water-filled impedance tube and the corresponding mode shapes are simulated using the finite element method. Two impedance tube configurations in air and three configurations in water are analyzed, and the maximum deviation from plane-wave behavior is reported for all modes. Furthermore, the modes in which the wave departs from plane-wave propagation are identified, and their mode shapes are presented. Finally, a waveguide with optimized dimensions and a broader operating frequency range than those reported in previous studies is proposed. In addition, plane-wave propagation in the proposed waveguide is examined under three conditions: rigid walls, dimensions suggested in the literature, and increased wall thickness.