We have developed and discussed the theory and applications of a physical-mathematical model of the dynamics of rain attenuation and have tested it as a rain attenuation prediction model in slant paths. Other parameters, however, such as fade durations and rates of change of fades, can be calculated. The main physical input is the 1-min rain rate time series of a site, which is converted to a rain rate space series along horizontal or slant paths by using an estimate of the storm translation speed &ngr; method known as ''synthetic storm technique.'' However, the long-term predictions are found to be insensitive to &ngr;. The vertical structure of precipitation is modeled with two layers. The model was tested against the probability distributions of rain long-term 11.6-GHz attenuation collected at the three Italian stations (Fucino, Gera Lario, and Spino d'Adda) during the SIRIO propagation experiment (13 years of data) for which concurrent rain rate time series are available. In the outage probability range 10-1 to 5¿10-3% defined the prediction error &egr;=(Ap-Am)/Am (where Am and Ap are respectively, the measured and predicted rain attenuations, dB), ⟨&egr;⟩=-10.6%, &sgr;=7.6% and rms=13%. Compared to nine other well-known prediction methods, the present model surmounts all of them in the three sites tested. ¿ American Geophysical Union 1996