Abstract: Based on the neutral axis theory of material mechanics, the shaft stiffness with a switching crack has been solved analytically. It has obtained the analytic expression of the stiffness in the direction of crack growth, its vertical direction and their coupling direction, while the corresponding stiffness in the fixed coordinate system is achieved. At the same time, the stiffness model of this paper is contrasted with cosine model and Zhu-Gao model. The conclusion indicates that: the stiffness curve in crack growth direction is a trapezoidal shape; the stiffness curve in its vertical direction is a symmetrical ladder shape; the stiffness curve in coupling direction is a sinusoid shape. In the fixed coordinate system the stiffness in three directions appears as complicated oscillating curves, the horizontal stiffness and vertical stiffness has some certain symmetry in one period, while the coupling stiffness has some certain inversion symmetry, and etc.