The multi-scale physical model for persistent heavy rainfall events (PHREs) in the Yangtze-Huaihe River Valley (YHRV), the energy conversion between systems of various scales, and the effects of eastward propagating convection systems from the eastern edge of Tibetan Plateau (TP) on precipitation in regions downstream have been summarized in this paper. To reveal the mechanisms sustaining the quasi-stable middle-latitude troughs and ridges over Eurasia, we analyze the energy dispersion of Rossby waves. The sources of the cold and warm air and their main transport paths are also discussed. The multi-scale physical model for PHREs in the YHRV is proposed. Quantitative calculation of energy conversion between systems of different scales show that the large-scale background circulation is the main energy source maintaining the sub-synoptic and/or mesoscale systems that directly induce heavy precipitation. Energy is transferred from the background circulation to the precipitation-related smaller-scale system through the downscaled energy cascade process of kinetic energy, which maximizes in the lower troposphere. The eastward propagation of convective systems from the eastern edge of the TP to the eastern coastal region is primarily attributed to a series of convective activities associated with several systems from west to east, including the mountain-plain solenoid between the Tibetan Plateau and Sichuan Basin, the southwest vortex, the mountain-plain solenoid between the second-step terrain and the eastern plains, the mesoscale vortexes, and convective systems to the east of the second-step terrain. In addition to the factors summarized in this paper, the PHREs in YHRV are also affected by many other factors, such as the Rossby wave sources associated with the multi-scale interaction, the effects of Rossby waves on synoptic systems, and the energy feedback of the mesoscale systems on their large-scale background circulations. These factors will be investigated further in the future.