A method is presented for calculating the effective gamma-quanta spect
ra for conditions of parallel-plate barrier geometry of irradiation fr
om an isotropic Co-60 source, when multiple Compton scattering plays t
he most important part in the process of propagation of gamma-radiatio
n. It is a version of the successive collision method, in which an act
ual gamma-quanta spectrum is expressed as the infinite sum of the part
ial spectra of gamma-quanta that undergo a certain number of Compton s
catterings. The convergence of this series of partial spectra is analy
tically proven for a real range of the energy changes.