This paper presents a comparative evaluation of elastic and viscoelastic solutions to identify more suitable and practical engineering solutions. Based on the viscoelastic solutions of a Kelvin's space half-infinite body, as an example, we analyzed the dynamic stress response under moving subway loads to illustrate the characteristics of dynamic stress, the stress path, and the principal stress axis rotations. By applying two solutions, we found the numerical results for the development trends of the dynamic stress state and principal stress axis rotation to be similar. We also found discrepancies in the dynamic stress of the ultimate state and stress path. Additionally, our results indicate that a viscoelastic solution is more applicable to actual working cases of long-term metro tunnel deformation in soft soil areas. Moreover, according to our analysis of viscoelastic solutions of dynamic stress characteristics under single-wheel loads, we found different feature coefficients to have different influences on stress characteristics.