The neutron Electric Dipole Moment Experiment at the Spallation Neutron Source requires an overall magnetic shielding factor of order 105 to attenuate external background magnetic fields. At present, the shielding design includes an external (room-temperature) multi-layer μ-metal magnetic shield, a cryogenic (4 Kelvin) Pb superconducting shield, and a cryogenic (4 Kelvin) ferromagnetic shield composed of Metglas ribbon. This research determined how to construct a Metglas shield using minimal material that produced axial and transverse shielding factors of ~267 and ~1500. In addition, the μ-metal and Metglas shields were modeled using finite element analysis. The FEA model includes external coils and their effect on the residual magnetic fields. This study will help with the design of the shielding.