The development of variable-order mapped infinite wave envelope elements for finite element modeling of acoustic radiation from turbofan nacelles is reviewed. These elements can be used outside of the near field as a nonreflecting boundary condition and as a finite-dimensional discretization of the infinite exterior domain for calculation of far-field acoustic radiation. The Kirchhoff method previously has been investigated in the context of the turbofan inlet radiation problem to extend a near-field solution to the far field. When the results of the mapped infinite wave envelope element analysis are compared with results of the Kirchhoff method, it is found that the mapped element formulation efficiently provides the acoustic far field, obviating the need to carry out an additional Kirchhoff integral formulation. Relative efficiencies are considered, and it is found that finite-dimensional discretization of the far field using mapped infinite elements is superior to the Kirchhoff formulation when radiation directivity in the entire far field is required.