The forward and backward projection of pressure fields from complex three-dimensional harmonically vibrating bodies is an important problem in noise control. A new generalized internal source density (GISD) method is presented to address the projection problem. The GISD approach is based on decomposing the pressure field on a closed surface of revolution in the fluid into a summation of circumferential orders where the pressure field for each order is associated with an internal linear distribution of ring sources on the axis of revolution. The axial variation of each source distribution is formulated as the solution of a mean square error problem and the resulting distributions can then be simply used to determine the entire external and/or surface pressure and velocity fields of the vibrating body. Analytical and numerical results are presented for several examples to illustrate the basic approach for bodies with different aspect ratios. Exact expressions for the source strength distributions for a sphere are developed and shown to have a vanishingly small region of support about the center of the sphere. For cylindrically shaped bodies with large aspect ratios, the spatial characteristics of the source strength distributions more closely match the normal velocity distribution.