An asymptotic analysis of interfacial stability with the surface tension anisotropy is derived for directional solidification of alloys. The zero and first order solution for multi-scale and the zero order solution for single-scale are obtained. The dispersion relation adapted to all wave-length is presented by combining the short and the long wave-length solutions. It was concluded that the zero order asymptotic solution is equivalent to constitutional undercooling theory and the first order solution is consistent with M-S theory. The instability zone of control parameter enlarges with the surface tension anisotropy,especially for the high temperature gradient and high pulling velocitycases.