Floating ice cover determines dynamic interaction between the ocean and the atmosphere, influencing the dynamics of the sea surface and subsurface waters, as the ice cover and the entire mass of water beneath it participate in the overall vertical motion. This paper examines the amplitude-phase structure of wave fields arising at the interface between ice and homogeneous water of finite thickness, generated by moving and stationary localized disturbance sources. The ice cover is modeled as a thin elastic plate with small deformations, while the plate is physically linear. Integral representations of the solution are obtained in the linear approximation, and the results of dispersion relations and phase patterns are presented for various wave generation parameters. It is shown that the main parameters determining the characteristics of the amplitude-phase structure of wave disturbances on the ice surface are ice thickness, velocity of the wave source, and oscillation frequency. Numerical calculations demonstrate that changes in source velocity, ice thickness, and oscillation frequency lead to a noticeable qualitative restructuring of the phase patterns of the excited far-field wave fields at the ice–water interface. The wave pattern of disturbances far from the appearing source of disturbances is a wave system of long- and short-wave packets, with shorter waves traveling at higher velocities and longer wave trains propagating at slower velocities. The spatial and temporal evolution of wave packets of ice surface disturbances propagating from the appearing source of disturbances is investigated.