A mathematical model for the radiation of baffled finite ducts is presented. This model was developed to be used for the design process of Magnetic Resonance Imaging (MRI) scanners. The added value of utilizing this model over using general purpose acoustics software is the increased insight into the acoustic phenomena in the baffled finite duct and the increased efficiency. The problem domain of the scanner was characterized as a finite duct with infinite flanges, acoustically excited by wall vibration. A mathematical model for this problem domain was developed, based on a model description of the acoustic field. The model was constructed by using a Fourier transformation technique for the Helmholtz equation and the velocity boundary conditions at the duct's wall. The diffraction of sound at the flanges was described with reflection coefficients. Two simultaneous matrix equations were found describing the acoustic field in the wall-driven baffled finite duct. Special attention was paid to the efficient implementation of the model. The physical and computational characteristics of the model were determined by parameter study and by comparison with Fourier Boundary Element Method (BEM) models of the MRI scanner. A good agreement was found between the results obtained with the baffled duct and the Fourier BEM models. Because of the direct relationship between design parameters and acoustic response, and because of the better numerical efficiency of the baffled duct model as opposed to the Fourier BEM models, the application of the baffled duct model in the design process is viable.