Viscoelastic materials are applied in several fields, and their relaxation characteristics are intricately related to the failure mechanism of sealing components and the generation of indentation rolling resistance in belt conveyors. Therefore, it is imperative to explore the relaxation characteristics of viscoelastic materials using characterization models. This article focuses on exploring these characterization models and the indentation rolling resistance of viscoelastic materials. The research comprises the following aspects: (1) A 2N + 2 element generalized Maxwell constitutive model is proposed for the relaxation behavior of viscoelastic materials to address the limitations of conventional relaxation models. (2) We conducted numerical calculations based on the relaxation modulus to solve the relaxation spectrum using several relaxation spectrum models. The findings showed that the model parameters were dependent on the testing time range. (3) The relationship between the indentation rolling resistance and relaxation model parameters was evaluated based on the theoretical foundation of the indentation rolling resistance calculation.