As it is well known, shrink fits exhibit a stress concentration at the hub edges that can cause the failure of such mechanical components. A method for reducing such a stress concentration is placing a contact ring between the hub and the shaft. To achieve the desired effect, the Young Modulus of the material used for the contact ring must be lower than the one used in the hub and the shaft. Unfortunately, there are no design methods for estimating the optimal dimensions or materials of the contact ring. To fill this gap, in this study, diverse numerical simulations by the finite elements method (FEM) were carried out considering different geometries and materials in order to obtain recommendations that allow mechanical designers to significantly reduce the stress concentrations in these components. According to the obtained results, a contact ring of 25% of the hub thickness allows to significantly reduce up to 40% of the stress concentration. In addition, a linear influence of the stress reduction with the Young modulus was found thereby, and the most recommendable material for the contact ring is the one with the lowest Young modulus. On the other hand, according to the obtained results, the influence of the Poisson coefficient can be considered negligible.