The Front End Enclosure (FEE) of the Linac Coherent Light Source (LCLS) is a shielding housing located between the electron dump area and the first experimental hutch. The upstream part of the FEE hosts the commissioning diagnostics for the FEL beam. In the downstream part of the FEE, two sets of grazing incidence mirror and several collimators are used to direct the beam to one of the experimental stations and reduce the bremsstrahlung background and the hard component of the spontaneous radiation spectrum. This paper addresses the beam loss assumptions and radiation sources entering the FEE used for the design of the FEE shielding using the Monte-Carlo code FLUKA. The beam containment system prevents abnormal levels of radiations inside the FEE and ensures that the beam remains in its intended path is also described. Show Partial Abstract