The Linac Coherent Light Source Matter in Extreme Conditions (MEC) Instrument is an X-ray instrument that will be able to create and diagnose high-energy-density matter. The MEC laser system can generate hard X-rays due to the interaction of the laser and the plasma. This paper summarizes results of the shielding calculations performed to evaluate the radiation hazards induced by this hard-X-ray source with the Monte Carlo code FLUKA. The dose rates and photon spectra due to this X-ray source are calculated at different locations with different shielding. The influence of the electron temperature on the source terms and the shielding effectiveness was also investigated.