Viscoelastic mechanics is an important research field in solid mechanics. The proper teaching of viscoelastic mechanics is crucial for students to grasp the related concepts. This paper uses the basic and classical Maxwell model in viscoelastic mechanics to illustrate the teaching process. Initially, the Maxwell model and its generalized expressions are introduced and derived from the basic viscoelastic components. Then, the classical Maxwell model is applied to the deformation of disordered solids by considering the characteristic time of activation of the deformation unit from the perspective of stress relaxation experimental curves of amorphous alloys. To deepen students' understanding and application of the model, the classical Maxwell model is further applied to practical cases and calculation exercises. This paper considers the Gauss distribution of the characteristic time of multiple parallel units in the generalized Maxwell model on a logarithmic time scale, which is highly valuable for studying the deformation of amorphous solids and teaching viscoelasticity theory. Compared to traditional viscoelasticity courses, this approach offers a comprehensive and practical learning experience for students.