QED-effects are known to occur in a strong laser pulse interaction with a counterpropagating electron beam, among these effects being electron-positron pair creation. We discuss the range of laser pulse intensities of J ≥ 5 · 10^22 W/cm2 combined with electron beam energies of tens of GeV. In this regime multiple pairs may be generated from a single beam electron, some of the newborn particles being capable of further pair production. Radiation back-reaction prevents avalanche development and limits pair creation. The system of integro-differential kinetic equations for electrons, positrons and -photons is derived and solved numerically.
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