Appropriate modeling of the interaction between wheel and terrain is a key element in simulating wheeled mobile robots (rovers) and analyzing their mobility on soft terrain. In this paper, experimentally validated semi-empirical terramechanics models are combined with an advanced multibody dynamics environment, CM-Labs’ Vortex, to achieve high-fidelity and real-time simulation of vehicles and rovers, operating on soft soil. A high-resolution heightfield is employed to model terrain-surface deformations and changes in hardening of soil under the wheel. As a result, the multi-pass effect is captured in our approach. For every wheel in contact with soft soil, unilateral contact constraints are added to the solver for the normal direction and some additional constraints for the motion in the tangent plane. This leads to the dynamics representation in the form of linear complementarity problems (LCP). The properties of the unilateral constraints are set based on the soil reactions computed from the terramechanics relations at every time step of the simulation. In addition, rigid obstacles are included using the standard unilateral point-contact constraints of Vortex. A collision detection algorithm identifies whether the wheel is in contact with the hard obstacle, soft soil or both, and appropriate constraints are added. Using LCP formulations to represent terrain reactions, our implementation effectively prevents overshooting of forces applied to the wheels and allows for stable simulation even at large time steps. Experimental investigation has been performed using a version of the Juno rover (Juno II), owned by the Canadian Space Agency (CSA) and developed by Neptec and Ontario Drive Gear (ODG). The analysis of the results shows good agreement between the experimental rover behaviour and the simulations.