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Interaction of a high-intensity optical laser with a solid target can generate an ionizing radiation hazard in the form of high-energy “hot” electrons and bremsstrahlung, resulting from hot electrons interacting with the target itself and the surrounding target chamber. Previous studies have characterized the bremsstrahlung dose yields generated by such interactions for lasers in the range of 1017 to 1022 W cm−2 using particle-in-cell code EPOCH and Monte Carlo code FLUKA. In this paper, electron measurements based on a depth-dose approach are presented for two laser intensities, which indicate a Maxwellian distribution is more suitable for estimating the hot electrons’ energy distribution. Also, transmission factors for the resulting bremsstrahlung for common shielding materials are calculated with FLUKA, and shielding tenth-value-layer thicknesses are also derived. In combination with the bremsstrahlung dose yield, the tenth-value layers provide radiation protection programs the means to evaluate radiation hazards and design shielding for high-intensity laser facilities.