Electron-positron pair creation is among the QED-effects known to occur in a strong laser pulse interaction with a counter-propagating electron beam. 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 γ-photons is solved numerically.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.