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An analytical solution to the scattering of an off-axis Gaussian beam incident on an anisotropic coated sphere is proposed. Based on the local approximation of the off-axis beam shape coefficients, the field of the incident Gaussian beam is expanded using first spherical vector wave functions. By introducing the Fourier transform, the electromagnetic fields in the anisotropic layer are expressed as the addition of the first and the second spherical vector wave functions. The expansion coefficients are analytically derived by applying the continuous tangential boundary conditions to each interface among the internal isotropic dielectric or conducting sphere, the anisotropic shell, and the free space. The influence of the beam widths, the beam waist center positioning, and the size parameters of the spherical structure on the field distributions are analyzed. The applications of this theoretical development in the fields of biomedicine, target shielding, and anti-radar coating are numerically discussed. The accuracy of the theory is verified by comparing the numerical results reduced to the special cases of a plane wave incidence and the case of a homogeneous anisotropic sphere with results from a CST simulation and references. [ABSTRACT FROM AUTHOR]