This paper focuses on developing an advanced analytical tire-terrain interaction model for full vehicle performance prediction purposes. The truck tire size 315/80R22.5 is modeled using the Finite Element Analysis (FEA) technique and validated against manufacturer experimental data in static and dynamic domains. While the terrain is modeled using Smoothed-Particle Hydrodynamics (SPH) technique and calibrated using experimental results of pressure-sinkage and direct shear tests. The contact between the FEA tire model and the SPH soil model is defined using the node symmetric node to segment with the edge treatment algorithm. The model setup consists of four tires appended back to back over a box filled with soil particles to represent a multi-axle off-road truck. The distances between the four tires are similar to the distances between the four axles of an off-road truck. The simulation running time is determined according to the time when the tires reach a steady-state depending on different operating conditions, such as speed, traffic, inflation pressure, vertical load, and steering angle in addition to soil characteristics such as cohesion, angle of resistance, and depth. The tires-terrain interaction simulations are performed over different types of terrains such as dry clay, dry sandy loam, 10% moist sand, 25% moist sand, and 50% moist sand soils at different operating conditions to determine the longitudinal and lateral forces of each tire. The data obtained from the simulations are further implemented into a Genetic Algorithm to develop explicit relationships between the forces and operating conditions. This research will further continue to predict the full vehicle performance over various terrains at several operating conditions.