High-field, high-speed Magnetic Resonance Imaging (MRI) generates high sound levels within and nearby the scanner. The mechanism and process that produces the gradient magnetic field (a cylindrical electro-magnet, called the gradient coil cylinder, which produces a spatially and temporally varying magnetic field inside a static background magnetic field) is the primary source of this noise. This noise can cause difficulties in verbal communication in and around the scanner, heightened patient anxiety, temporary hearing loss and possible permanent hearing impairment for health care workers and patients. In order to effectively suppress the sound radiation from the gradient coil cylinder the sound field within and nearby the gradient coil needs to be characterized. This characterization may be made using an analytical solution of the sound pressure field, computational simulation, measurement analysis or some combination of these three methods. This paper presents the computational simulation and measurement results of a study of the sound radiation from a head and neck gradient coil cylinder within a 4 Tesla MRI whole body scanner. The measurement results for the sound pressure level distribution along the centerline of the gradient coil cylinder are presented. The sound pressure distributions predicted from Finite Element Analysis of the gradient coil movement during operation and subsequent Boundary Element Analysis of the sound field generated are also presented. A comparison of the measured results and the predicted results shows close agreement. Because of the extremely complex nature of the analytical solution for the gradient coil cylinder, a treatment of the analytical solution and comparison to the computational results for a simple cylinder vibrating in a purely radial direction are also presented and also show close agreement between the two methods thus validating the computational approach used with the more complex gradient coil cylinder.