The three-phase transformer is a core component of the power system. As there are electromagnetic couplings within and between windings, the complexity of the inter-turn fault analysis increases. An accurate transformer model benefits the analysis of short-circuit faults. Transformer models mainly include finite element models and electromagnetic transient models. The simulation time of the finite element model is positively related to the complexity of the model. Therefore, the finite element model has the disadvantage of long simulation time. Electromagnetic transient model can be divided into circuit model and magnetic circuit model. On one hand, circuit models cannot directly describe the physical properties of three-phase transformers. On the other hand, the accuracy of magnetic circuit models depends on the accurate analysis method of the transformer magnetic circuit structure. While the analysis of the interphase coupling relationship of three-phase core-type transformers is difficult. In this paper, the interphase coupling characteristics of three-phase core-type transformers are fully considered. A mathematical model is constructed that can accurately characterize the physical properties of transformers. The accurate representation method of interphase coupling relationship of three-phase core-type transformers is proposed. Finite element model and electromagnetic transient model are used to conduct inter-turn fault tests to verify the correctness of the model. The new model provides a model foundation for transformer inter-turn fault research.