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This paper presented the PEEC models for 3D metallic plates with symmetry and/or anti-symmetry. These plates of concern were normally used for magnetic shielding, and were made of either conductive material or linear magnetic material. The distribution of both induced current and magnetization in the plates was examined, and the symmetrical and anti-symmetrical prosperities in typical shielding structures were identified. Reduced system matrix equations were provided. Using the loop analysis technique, the matrix equation can be reduced to one sixth approximately in size if these properties are fully taken into account. A shielding problem can be then solved at the reduced cost without loss of accuracy. The proposed modeling techniques have been tested numerically, and validated with a commercial FEM code.