The notch is not only one of the primary reasons of component fracture, but also the key factor in life assessment of shaft. The stress and displacement field near the tip of annular notch should be obtained at first for safe design and life assessment. A quadric coordinate system suited for annular notch is proposed and the stress and displacement component of cylindrical shaft with annular notch are derived by using the modified Galerkin displacement function. This method can be used to solve various problems of cylindrical shaft with annular notch by selecting an appropriate displacement function and provides the basis for safe design and life assessment of this kind of components. A solution of torsional problems of cylindrical shaft with annular notch is calculated as a demonstration of the method presented.