In this study, the effects of frequency, height and wavelength of progressive gravity waves on vibration and energy absorption of the single- and two-degree of freedom Bristol oscillating cylinder systems have been investigated experimentally and numerically in different depth of water. The experiments were carried out in channel equipped with both a paddle-type wave-maker and wave features measurement tools. Numerical simulations were conducted in COMSOL software assigned to simulate interactions between physical environments for turbulent flow. Making a comparison between the numerical and experimental conclusions compared to the other researchers' results demonstrates a desired matching in a wide range of waves' parameters. It can be seen in findings that changing in depth of submerged objects from free surface of water has considerable influence on their vibration behavior, so that by rising in depth, the oscillations amplitude increases to a maximam and then decreases. The obtained results indicate the different effects of relative depth under the submerged buoy on the efficiency of the single- and two-degree of freedom systems; so that increasing water height causes rise in the efficiency of single degree of freedom systems, but it doesn't have considerable influence on two degree of freedom systems. The results also show that expanding the wave-maker frequency for a constant height of water in channel causes to rise in energy and height of the generated waves so that oscillations amplitude of submerged buoy rise in vertical and horizontal line.