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This paper presents an application of the element-free Galerkin (EFG) method in modeling nondestructive evaluation of civil structures using microwaves. Use of the EFG method avoids mesh generation that is cumbersome in conventional finite element methods when complex geometries are to be modeled. The efficiency of the EFG method becomes more obvious if the numerical model is iteratively used in an inversion process to reconstruct object geometries because re-meshing is avoided. Computational results are presented in this paper and validated by comparing with analytical solutions of canonical scattering problems