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A new traction model was developed to predict traction for agricultural drive tires operating in soil with incomplete lug penetration. The model uses the Bernstein equation to predict the depth of penetration of the lug and undertread of the tire. The maximum shear stress is then calculated according to the Mohr-Colomb equation. The shear stress was predicted along the length of the tire footprint by using the Janosi-Hanamoto relationship. The gross traction was predicted by integrating the shear stress over the area of the tire. The new model more closely approximated the test data than any of the other commonly used models. In addition, the new model and experimental data showed that tractive performance in soft soil can be better than tractive performance on firm soil due to increased lug penetration.