Power transformers serve as crucial hub equipment in modern power systems, hence their reliability and security have been the major concern to the power industry. The vibration of the cores of the transformers due to magnetostriction can result in severe security issues, and is one of the dominant origins of the noise during the operation of the transformers. In this manuscript, we take a 10 kV transformer as an example to establish a magneto-solid-acoustic coupling finite element model of the transformers, taking into account the magnetostrictive properties of the cores. The reliability and accuracy of the model is then demonstrated via A posteriori error estimation. The vibration noise of the reference transformer is then investigated based on the verified model.