This thesis comprises a body of work that investigates the electromechanical vibration properties of transformer cores. Two extensive field tests were conducted to characterise transformer noise and vibration. As the source of vibration excitation, the magnetic field of the transformer core is investigated based on the online modelled hysteresis loops. An engineering model for the electromagnetic force at the structural discontinuities, as one of the major excitation force, is developed. The frequency response function of the transformer core, from force to vibration, is simulated efficiently and accurately using equivalent Young's modulus and finite element method.