The influence on ray propagation of including both attenuation and beam displacement at the bottom of a shallow‐water isospeed channel is determined. Attenuation is incorporated using the Mackenzie‐bottom model, rather than the commonly used Rayleigh reflection theory. Properties of displacement are studied as a function of launch angle and parameters such as bottom‐to‐water density, channel depth in wavelengths, and channel aspect ratio. Differences in beam displacement for the two bottom models are shown to affect the number and geometry of rays between surfaced source and receiver. Formulas for per‐ray amplitude and phase shift and for incoherent total‐field intensity are developed. Comparisons are made between these quantities for both modified and classical ray theory with a Mackenzie bottom, and also for both Mackenzie‐ and Rayleigh‐bottom models using modified rays. Numerical computations show significant phase and amplitude differences arising in both types of comparisons.