In this article, an extension of the finite element technique to the analysis of the acoustic radiation is presented. In the proposed approach, the acoustic domain is split into two parts by an arbitrary artificial boundary enclosing the radiating surface. Then the unbounded medium is discretized with finite elements consisting of only one or two rows in the radial direction up to the artificial boundary. To represent the farfield behaviour, the constraint equation specified on the artificial boundary is formulated with a more straightforward boundary integral equation, in which the source surface coincides with the radiating surface discretized with boundary elements. To ensure the uniqueness of the numerical solution, the composite Helmholtz integral equation proposed by Burton and Miller was adopted. Due to the avoidance of singularity problems inherent in the boundary element formulation, this method is very efficient and easy to implement in an isoparametric element environment. In numerical experiments involving spherical and cubical radiators, it has been demonstrated that the proposed method eliminates the difficulties when the FEM handles the exterior acoustics. It should be noted that the method can be extended to the computation on other branches of the classical field theory.