A toroidal magnet system consisting of six superconducting coils is being built for the Jefferson Lab 12 GeV accelerator upgrade project. This paper details the analysis of eddy current effects during a quench event on the aluminum thermal shield. The shield has been analyzed for mechanical stresses induced as a result of a coil quench as well as a fast discharge of the complete magnet system. The shield has been designed to reduce the eddy current effects and result in stresses within allowable limits.