Cutting and punching of the electrical steel can cause edge burrs which lead to interlaminar short circuits between the laminations. In this paper, based on an equivalent electric circuit of the eddy current path, an analytical method has been developed to estimate the eddy current power loss of the magnetic cores, caused by the interlaminar faults, in a wide range of flux density and magnetizing frequency. Important factors, such as skin effect, nonuniform flux density distribution, complex relative permeability, and the nonlinear relation of, which are often neglected in the literature, are highlighted. Fundamental concepts of the interlaminar fault and its consequences, the effect of interlaminar faults on the configuration of magnetic cores, and finite-element method verification are presented in this Part I paper. Modeling of eddy current, together with experimental results of eddy current measurements of packs of shorted laminations, are reported in Part II.