This paper introduces a hierarchical sequential arbitrary Lagrangian-Eulerian (ALE) model for predicting the tire-soil-water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid-infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two-phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator-split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire-soil-water interaction both close to the contact and in the far field. The presented ALE model for tire-soil-water interaction provides the essential basis for future applications, for example, to a path-dependent frictional-cohesive response of the consolidating soil and unsaturated soil, respectively.