An analytical model has been developed for the pile vibration and consequent sound pressure and particle velocity radiated underwater when an offshore cylindrical pile is struck by a drop hammer. The model, which is based on the coupled equations of motion for axial and radial vibration of a thin cylindrical shell, yields frequency-dependent phase velocity and attenuation of these vibrations. The amplitude of the pulse of axial and radial displacement that travels down a pile following an axial impact is described in terms of the hammer properties. Solutions are obtained for the radiated sound pressure and particle velocity, using Junger and Feit's Transform Formulation of the Pressure Field of Cylindrical Radiators [(Acoustical Society of America, New York, 1993), p. 216]. The model is applied to published data on radiated noise from offshore driving of a steel pile. The modeled pressure waveforms at 12-m horizontal range and at 9 hydrophone depths correlate significantly with the measured waveforms. The modeled pressures of the initial positive peaks (appropriately low-pass filtered) agree with data to within 1 dB. The initial negative peaks however exceed the data by up to 7 dB, and as hydrophone depth increases, the model negative peaks have a maximum at 7 m, whereas the data have a maximum at 9 m.