A one-dimensional Winkler foundation and a generalized viscoelastic Maxwell solid model of the belt backing material are used to determine the resistance to motion of a conveyor belt over idlers. The viscoelastic material model is a generalization of the three-parameter Maxwell model that has previously been used to predict the effective frictional coefficient of the rolling motion. Frequency, or loading rate, and temperature dependence of the material properties are incorporated with the time/temperature correspondence principle of linear viscoelastic materials. As a consequence of the Winkler foundation model, a normalized indentation resistance is independent of the primary belt system parameters - carrying weight per unit width, idler diameter and backing thickness - as is the case for a three-parameter viscoelastic model. Example results are provided for a typical rubber compound backing material and belt system parameters.