This paper focuses on analysis of the cornering characteristics of an off-road truck tire running under several operating conditions over different soils. The finite element analysis (FEA) method is used to model the Goodyear RHD 315/80R22.5 truck tire, and the smoothed-particle hydrodynamics (SPH) method is used to model the soil. The goal of this research is to provide a virtual testing environment in Pam-Crash software as an alternative to actual tests for FEA and SPH analyses of rolling tire interactions on deformable terrains. The study on the effects of different operating parameters on the cornering performance combined with the sensitivity study can be of interest to tire engineers or vehicle engineers because they provide insight into the design and real-time behavior of a vehicle. Tire and soil models are validated using experimental data and published measurements, showing good agreement. The tire–soil interaction is investigated under different tire conditions, such as longitudinal speed, inflation pressure, vertical load, and slip angle, and under various soil characteristics, such as cohesion, internal friction angle, and rut depth. Cornering force, self-aligning moment, and overturning moment are studied as the fundamental cornering characteristics that affect truck lateral stability and control. Owing to the excessive computational demands posed by the FEA-SPH tire–soil models, we propose unique mathematical relationships for estimating the cornering characteristics of free-rolling as well as driven truck tires in an efficient manner. The genetic algorithm (GA) technique is used to develop relationships between the cornering parameters and operating conditions. We conclude that the identified mathematical relationships could provide very good estimations of the cornering characteristics under a broad range of operating conditions and soils. The GA equations will ultimately be implemented into a full vehicle model to evaluate the full vehicle performance.