The Generalized Internal Source Density (GISD) method [P. R. Stepanishen, J. Acoust. Soc. Am. 102, 1955–1963 (1999)] is used to backward project acoustic harmonic pressure fields from an external measurement surface of revolution enclosing the finite three-dimensional vibrating body that generated the field. Both the normal velocity and pressure fields on the vibrating surface can be readily reconstructed using the method. The GISD method is based on first decomposing the acoustic field on the measurement surface into a modal summation of circumferential orders, where each modal pressure field is associated with an internal linear distribution of ring sources on the axis of revolution of the measurement surface. Each modal linear distribution of ring sources is evaluated using Singular Value Decomposition (SVD) methods. A brief review of the method is presented and discussed and then numerical results are presented to illustrate the accuracy of the method for a spherical shell and finite cylindrical shells with hemispherical end caps. The results show excellent agreement with the prescribed normal velocities and associated pressure fields over a wide frequency range.