The method proposed in this paper provides a computational method for implementing the Helmholtz integral formula for acoustic radiation and scattering problems associated with arbitrary shaped three‐dimensional bodies. In particular an isoparametric element formulation is used in which both the surface geometry and the acoustic variables on the surface of the body are represented by second‐order shape functions within the local coordinate system. A general formula for the surface velocity potential and the exterior field is derived. This result is applicable to nonsmooth bodies, i.e., it includes the case where the surface may have a nonunique normal (e.g., at the edge of a cube). Test cases are shown involving spherical, cylindrical, and cubical geometry.