Based on a hybrid superposition of an indentation contact and a rolling contact an analytical procedure is developed to evaluate the effects of surface adhesion during steady-state rolling contact, whereby two analytic solutions have been obtained. The first solution is a Hertz-type rolling contact between a rigid cylinder and a plane strain semi-infinite elastic substrate with finite adhesion, which is a JKR-type rolling contact but without singular adhesive traction at the edges of the contact zone. The second solution is of a rolling contact with JKR singular adhesive traction. The theoretical solution indicates that, when surface adhesion exists, the friction resistance can be significant provided the external normal force is small. In addition to the conventional friction coefficient, the ratio between friction resistance force and normal force, this paper suggests an “adhesion friction coefficient” which is defined as the ratio between friction resistance force and the sum of the normal force and a function of maximum adhesive traction per unit area, elastic constant of the substrate, and contact area that is characterized by the curvature of the roller surface.