The ELI (Extreme Light Infrastructure) Beamlines facility in the Czech Republic, which is planned to complete the installation in 2015, is one of the four pillars of the ELI European project. Several laser beamlines with ultrahigh intensities and ultrashort pulses are foreseen, offering versatile radiation sources in an unprecedented energy range: laser-driven particle beams are expected to range between 1 and 50 GeV for electrons and from 100 MeV up to 3 GeV for protons. The number of particles delivered per laser shot is estimated to be 10(9)-10(10) for the electron beams and 10(10)-10(12) for the proton beams. The high energy and current values of the produced particles, together with the potentiality to operate at 10 Hz laser repetition rate, require an accurate study of the primary and secondary radiation fields to optimize appropriate shielding solutions: this is a key issue to minimize prompt and residual doses in order to protect the personnel, reduce the radiation damage of electronic devices and avoid strong limitations in the operational time. A general shielding study for the 10 PW (0.016 Hz) and 2 PW (10 Hz) laser beamlines is presented here. Starting from analytical calculations, as well as from dedicated simulations, the main electron and proton fields produced in the laser-matter interaction have been described and used to characterize the "source terms" in full simulations with the Monte Carlo code FLUKA. The secondary radiation fields have been then analyzed to assess a proper shielding. The results of this study and the proposed solutions for the beam dumps of the high energy beamlines, together with a cross-check analysis performed with the Monte Carlo code GEANT4, are presented. (C) 2012 Elsevier B. V. All rights reserved.