The Helmholtz Equation Least Squares (HELS) method previously derived by Wang and Wu (1997) and Wu and Wang (1998) is used to reconstruct the radiated acoustic pressure fields from a complex vibrating structure. The structure under consideration is of the form of a real, full-size four-cylinder engine designed for a passenger vehicle. To simulate sound radiation from a vibrating engine block, harmonic forces are assumed to exert on two arbitrarily selected sides. The resulting vibration responses are solved by using finite element method (FEM) through a commercial software package, I-DEAS Master Series 5®. Once the normal component of surface velocity distribution is determined, the surface acoustic pressures are calculated by the Helmholtz-Kirchhoff integral theory using the standard boundary element method (BEM) codes. The radiated acoustic pressure fields are then calculated by the Helmhollz-Kirchhoff integral formulation. The results thus obtained are taken as the input to the HELS formulation to reconstruct the surface and field acoustic pressures. Numerical results show that good agreement can be obtained with relatively few measurements in the field. Further, sound pressures over the entire surface of a complex structure can be reconstructed This method is shown to be very effective at low to mid frequency ranges. The effectiveness of the HELS method may deteriorate, however, as the frequency increases. This is because the HELS method is based on an expansion of spheroidal functions, which converges slowly at high frequencies. Nonetheless, in engineering practice noise diagnostics are often carried out in the low to mid frequency ranges. Under this circumstance, the present HELS method can become a robust and effective noise diagnostic tool.