The development of new technologies for broadband wireless access, using increasingly higher frequencies, points to the necessity of more accurate methods for rain attenuation, that represents the most serious impairment for radio systems operating in frequencies above 10 GHz. This work presents semi-empirical models for the prediction of rain attenuation in terrestrial and satellite links. The models were developed using data obtained in concurrent measurements of rain attenuation and point rainfall rate in different regions of Brazil. Some of these measurements were performed as part of this work and some were already available from previous measurements campaigns. Data available in the UIT-R data banks of propagation measurements were also used, in order to develop global methods. The models that have been developed allow the prediction of the cumulative probability distribution of rain attenuation from the cumulative distribution of point rainfall rate in the region of the link. Although several methods with these purpose can be found in the technical literature, the ones developed in this work present some important features that are not found, as a whole, in any of those models: they use the full rainfall rate distribution over the entire range of time percentages of interest; the terrestrial and satellite models are consistent, that is, the elements used in the terrestrial prediction model are kept in the satellite prediction model that involves a mor complex geometry. Besides that, the models proposed show an excelent performance in terms of prediction error, when compared with measured data.