Thermal contact resistances between solid materials constitute a major challenge in numerous industries. Most works on this subject deal with the modeling of the contact resistance between flat surfaces. A microscopic modeling of the cylinder-cylinder contact in steady state is proposed in this paper. This three-dimensional model is completely analytical. It first allows a representation of the thermal contact resistance using a three resistance network: the constriction resistance is thus pinpointed. It also shows that. generally, the cylinder-cylinder constriction resistance can be replaced bq-a plane-plant constriction resistance: this result allows an extension of correlations relative to plane-plane models to the cylinder-cylinder case.