In this paper, the fully-coupled rolling contact problem between a rigid cylinder and an orthotropic medium is investigated. The governing equations are developed analytically; then, a numerical method, the Gauss-Chebyshev method, is used to solve the coupled integral equations. The rolling contact problem is solved by assuming a central stick zone accompanied with two slip regions. The main purpose of this study is to obtain the surface stresses in the contact area and investigate the effect of material orthotropic properties such as shear parameter and stiffness ratio and also the coefficient of friction on these contact stresses. In addition, the subsurface stresses in the orthotropic medium are determined and a parametric study, was subsequently executed. The current paper shows that the orthotropic parameters and the coefficient of friction significantly influence the contact surface stresses and the distribution of the interior field stresses. By appropriately choosing the values of these parameters, the stresses will decrease; thus, the failure behavior of the orthotropic medium improves. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim