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The amorphous alloy transformer with three-dimensional wound core (TDWC) is a new type of transformer structure. Compared with the traditional three-phase five-column transformer with planar wound core (PWC), the TDWC structure exhibits a fully symmetrical magnetic circuit, resulting in enhanced short-circuit withstand capability. However, the vibration noise of the core becomes a significant engineering challenge in the design and manufacturing process due to the larger magnetostrictive coefficient of the amorphous alloy. This study establishes a magnetic-mechanical coupling mathematical model for amorphous alloy TDWC considering the magnetostrictive effect. Three-dimensional finite element analysis (FEA) is adopted to calculate the flux and vibration displacement distribution of the TDWC. Additionally, an experimental validation is conducted on a 200kVA amorphous alloy TDWC prototype to verify the accuracy of the model. Furthermore, a comparison with the PWC prototype demonstrates that the TDWC structure can effectively reduce surface vibrations, and the dominant frequency distribution law of vibration displacement at different positions of the TDWC structure is revealed, providing a foundation for the design of vibration reduction and noise control for TDWC.