This paper presents a new mathematical model of a Jeffcott rotor within a snubber ring with anisotropic support. The derivation and validation of the model are based on an experimental rig designed and developed in Aberdeen University. Special attention is given to the estimation of the physical parameters of the snubber ring support, which reveals the presence of damping effects that are incorporated in the mathematical model. Furthermore, the numerical implementation of the model is described and mathematically justified in detail. The experimental investigation shows a sequence of different dynamical scenarios obtained under variation of the rotational speed, which in turn is satisfactorily reproduced by the theoretical model. The experimental and numerical results demonstrate the predictive capabilities of the model around the onset of impacts between the rotor and the snubber ring, which is one of the most common unwanted phenomena encountered in industrial applications of rotating machinery.