A method of a simulation of radiation fallout concomitant atmospheric liquid precipitations is proposed. The fallout is reconstructed from observed gammas through a numerical solution of the first kind Volterra integral equation describing variation of nuclide amount produced by precipitating 214 Pb and 214 Bi. Application of the method is considered on an example of rainfalls in Brazil. There were observed short fallout enhancements in the initial phases of the rains. It was demonstrated that nuclide quantity per unit of precipitated water decreases with increasing rainfall rate. The results obtained are compared with other observations and models.