More and more solid-state magnetic field sensors such as Hall devices are used in eddy current inspection (EC) to acquire magnetic field signals. This work extends the previous analytical model, i.e. 2D Extended Truncated Region Eigenfunction Expansion (ETREE) of EC, and focuses on establishment of 3D ETREE of multi-frequency eddy current inspection (MFEC) on stratified conductors, while taking into account the solid-state magnetic field sensors for field quantification and rectangular coils for field excitation. 3D Finite Element Modelling (FEM) and a hybrid modelling are adopted for verification of the established model. It has been noticed that the 3D ETREE implements the fast and accurate computation of magnetic field signals of MFEC. Following that, the directional characteristics of EC with rectangular excitation coils are investigated, which reveals that the coil width contributes more to the measurement sensitivity than the coil length, and benefits the evaluation of defects and anisotropic conductivity profile of conductors in the follow-up study.