To achieve precise analysis of magnetic flux distribution rules and magnetostrictive effects in transformer cores, this study constructs a magnetic circuit model that accounts for both rolling and transverse rolling directions, alongside a vibration circuit model, and adopts a frequency-domain calculation approach for fast solution. Firstly, based on the structural characteristics the core, the magnetic flux path in the lap area was deduced, and an equivalent two-port model of magnetic resistance in the lap zone was constructed, which was applied to a magnetic circuit model considering two directions; secondly, based on the principles of electromechanical analogy and magnetic vibration coupling theory, an equivalent vibration circuit model in a two-port cascade form was formed through infinitesimal processing; finally, a vibration acquisition platform for the transformer core’s magnetostrictive effect was built to conduct vibration measurement experiments on the core and perform time-domain and frequency-domain analyses. The simulation model was consistent with the experimental results, and the computation speed could reach a second-level, validating the effectiveness of the method.