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Summary In this paper, the coupling of the improved interpolating element‐free Galerkin (IIEFG) method and the variable‐order infinite acoustic wave envelope element (WEE) method is studied. A coupled IIEFG‐WEE method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages. The coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the IIEFG and WEE domains. In the IIEFG domain, the improved interpolating moving least‐squares (IIMLS) method is used to form the shape functions satisfying the Kronecker delta condition while nonsingular weight functions can be used. The impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated. The numerical results show that the coupled IIEFG‐WEE method can take full advantage of both the IIEFG and WEE methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the WEE. The experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain.

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