Rheological models capture the behaviour of soil structures and effectively evaluate the response of various transport corridors. These models represent the elastic and plastic behaviour of a structure. This paper reviews several rheological models that incorporate elasticity, viscosity, and plasticity principles. The review encompasses various rheological models developed as viscoelastic, elastoplastic, viscoplastic, elastoviscoplastic and viscoelastoplastic models, specifically for a better understanding of high-speed rail dynamics. Analytical solutions for these models are elaborated, focusing on the behaviour of soil structures and the interaction of layers, particularly in scenarios involving two or more layers. Additionally, detailed discussions cover the results and interpretations of various studies on these rheological models.