The problem of a rigid cylinder rolling on the surface of a viscoelastic solid is solved in an approximation in which inertial forces are neglected. With the introduction of viscoelastic effects, the symmetry associated with the corresponding elastic problem is destroyed, and in particular the cylinder motion is impeded by a resistive force. For a standard linear solid, the resulting coefficient of friction, a function of the rolling velocity V, tends to zero for small and large values of V, and attains a single maximum at an intermediate value.