The underwater noise from offshore pile driving has been getting increasing attention due to its deleterious effects on marine animals. Two models are established to investigate the influence of the cushion parameters, including stiffness and restitution coefficient, on the underwater sound radiation. The first model, based on a nonlinear finite difference formulation, is used to compute the impact force on the pile head and the soil penetration for a single impact. The underwater sound

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... radiated from the cylindrical pipe pile can be predicted by the second model based on a semi-analytical variational formulation. For the examined pile, the cushion can dramatically reduce the high-frequency underwater noise. A proper cushion reduces the peak sound pressure level by 17 dB but hardly reduces the soil penetration depth for each impact. The research can provide noise reduction designing schemes for pile driving system by choosing appropriate cushions based on prediction of underwater noise and soil penetration.