Transverse shaft cracks are one of the most dangerous malfunctions of the rotating machines, including turbo- and hydrogenerators, high-speed machine tool spindles, etc. The undetected crack may grow slowly and not disturb normal machine operation. However, if it extends to a critical depth, the immediate shaft fracture may completely damage the machine, resulting in a catastrophic accident. Therefore, in-depth knowledge of the crack propagation process is essential to ensure reliable and safe operation of rotating machinery. The article introduces a new model of the propagating shaft crack. The approach is based on the rigid finite element (RFE) method, which has previously proven its effectiveness in the dynamical analysis of numerous complicated machines and structures. The crack is modeled using several dozen spring-damping elements (SDEs), connecting the faces of the cracked section of the shaft. By controlling the exact behavior of individual SDEs, not only the breathing mechanism, but also the crack propagation process can be simply introduced. In order to accomplish this, the stress intensity factors (SIFs) along the crack edge are calculated using the novel approach based on the modified virtual crack closure technique (VCCT). Based on the SIF values, the crack propagation rate is calculated from the Paris law. If the number of load cycles is greater than the constantly updated threshold number, then the crack edge is shifted by a small increment. This way, starting from the first initially cracked SDE, the crack is extended little by little, continuously changing its shape. The approach is illustrated with numerical results, demonstrating the changes in the rotor vibration response and in the crack shape and also explaining some issues about the breathing mechanism due to the propagating shaft crack. The increasing amplitude of the 2X harmonic component is recognized as an evident propagating crack signature. The numerical results correspond well with the data reported in the literature. The RFE model of the rotor is validated by comparing the vibration responses obtained experimentally and numerically. A good agreement between these data confirms the correctness and accuracy of the proposed model. The suggested approach may be utilized for a more reliable dynamic analysis of the rotating shafts, having the potential to experience propagating transverse cracks.