A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction to efficiently compute normal and shear stress distributions in the contact area. The authors propose a velocity field in the vicinity of the contact area based on the physical nature of the problem. Thereupon, the incremental changes to the stress field are computed by resorting to elastoplasticity theory and an appropriate already existing constitutive relation for soil. The proposed approach leads to results that agree well with those obtained using well-established terramechanics models, while addressing some of their shortcomings. In addition, the proposed approach uses generalized velocities of the wheel as inputs, which makes it compatible with dynamic models of multibody systems. The dynamic slip-sinkage behavior of the wheel and the semielliptical shape of the normal stress distribution under the wheel are natural outcomes of the proposed model. Experimental investigation under various ranges of wheel slippage shows good agreement with the data available in the literature.