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Electrical impedance tomography (EIT) shows the conductivity distribution through the cross-section of a body part. It is reported that the image reconstruction is distorted considerably when the boundary shape is considered to be more elliptical than circular in a thorax model. The elliptic geometry model, which constructs more general structure, reduces the amount of problems and ensures more accurate results about perceiving inhomogeneities. In this study, the forward problem of EIT is analyzed under elliptical and circular frameworks by using an analytical and finite element method. The analytical solution defined for elliptic geometry is improved by applying the conformal transformation to the forward problem.