A first-kind integral equation relating the surface contact pressure to surface displacement is used to form an iterative algorithm which efficiently solves the problem of steady rolling of a cylinder on a viscoelastic half-space. The immediate solution is the contact pressure, but the quantity of interest is the friction coefficient (ratio of drag force to normal force), or effective resistance to rolling motion, which is readily obtained from the contact pressure. The so-called generalized N-parameter Maxwell model is used to characterize the rheology and is quite general and capable of representing realistic polymeric, elastomeric and rubber compounds. An iterative algorithm, like the Newton Raphson method, is used to obtain consistent equilibrium values of the contact stress profile and surface displacement for a given total resultant load. The friction coefficient is subsequently determined by integration of the interface pressure about the center of the rolling cylinder. As the employed integral equation formulation is in terms of the creep functions, a conversion of the creep parameters to relaxation parameter is also required. Results are provided for a typical rubber compound, showing the effects of velocity and applied load on friction coefficient.