In this paper, the effects of a breathing crack on the vibratory characteristics of a rotating shaft are investigated. A new, simple and robust model composed of two rigid bars connected with a nonlinear flexural spring is proposed. The nonlinear spring, located at the cracked transverse section position, concentrates the global stiffness of the cracked shaft. The breathing mechanism of the crack is described by a more realistic periodic variation of the global stiffness depending not only but substantially on the system vibratory response. It is based on an energy formulation of the problem of 3D elasticity with unilateral contact conditions on the crack lips. A possible partial opening and closing of the crack is considered which makes the approach more appropriate for deep cracks modeling. The harmonic balance method, direct time-integration schemes and nonlinear dynamics tools are used to characterize the global dynamics of the system. The effects of the crack depth and rotating frequency have been meticulously examined and it was found that the cracked shaft never exhibits chaotic or quasi-periodic vibratory response.