In this talk, the problem of SH-wave scattering by a circular hole buried in infinite functionally graded materials (FGM) is solved by using the null-field boundary integral equation method (null-field BIEM). For the considered FGM, the patterns of the shear modulus and the density are the form of exponential variation. Therefore, the governing equation for the time-harmonic motion is not a typical Helmholtz equation. By using the change of variables, the original governing equation can be transformed into the Helmholtz equation. The Neumann boundary condition due to the traction free condition is transformed into the Robin boundary condition. Therefore, the null-field BIEM can be straightforward employed to solve the problem of SH-wave scattering in the FGM. Using the degenerate kernel and the Fourier series to substitute for the closed-form fundamental solution and boundary densities, the semi-analytical solution can be obtained. In addition, the problem of SH-wave scattering by a circular hole buried in semi-infinite FGM is also considered. By using the image method, the semi-infinite plane problem containing a circular hole is transformed into the infinite plane problem containing two identical circular holes. The other key point is that the functions of the shear modulus and the density are also imaged. Finally, all numerical results are compared well with those of numerical results by using the conventional boundary element method (BEM) with the constant element scheme. Not only the displacement field of the whole domain but also the dynamic stress concentration factor along the circular hole is presented. The effect of the non-homogeneous parameter of materials is also considered.