A method for reconstructing the acoustic field on the surface of a vibrating object based on measurements of the radiated acoustic pressure includes solving the Helmholtz equation directly using the expansion of a set of independent functions that are generated by the Gram-Schmidt orthonormalization with respect to the particular solutions to the Helmholtz equation. The coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points. The errors involved in these coefficients are minimized by the least squares method. Once these coefficients are specified, the acoustic pressure at any point, including the source surface, is completely determined.