An advanced computational method is presented for calculating the sound radiated by vibrating engine of arbitrary shape. The method is based on the numerical evaluation of the Helmholtz Integral Equation. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the vibrating body are represented by second order shape functions within the local coordinate system. The formulation includes the case where the surface may have a non-unique normal (e.g. at edges or corners). A general result for the surface and field velocity potential is derived. Test cases involving spherical geometry are given for a pulsating sphere and for an oscillating sphere in which the analytical solutions are known. Examples for bodies with edges and corners are shown for the problems of radiation from a circular cylinder and from a pulsating cube.