Formulae for the leading vectorial term of the qS wave Green function in an unbounded inhomogeneous weakly anisotropic medium, obtained by using the so-called quasi-isotropic (QI) approximation, are presented. The QI approximation should be used for study of qS waves in regions, in which the difference between phase velocities of the two qS waves is small, e.g., in weakly anisotropic media. In such regions, the standard ray method for anisotropic media does not work properly and should be substituted by the QI approximation. The formulae for the leading vectorial term of the qS wave Green function in the QI approximation are regular everywhere except singular regions of the ray method for isotropic media. In the limit of infinitely weak anisotropy, the QI formulae smoothly converge to formulae for isotropic media. For stronger anisotropy, the QI formulae yield results, which can be matched with solutions of the standard ray method for anisotropic media.