This paper focuses on the modeling process of incorporating inflation pressure into the UniTire model for pure cornering. Via observing and manipulating the tire experimental data, the effects of inflation pressure on the tire cornering property are analyzed in detail, including the impacts on cornering stiffness, the peak friction coefficient, the curvature of transition region and the pneumatic trail. And the brief mechanism explanations are also given for some of these impacts. The results show that some effects of inflation pressure are similar to that of vertical load on the non-dimensional tire cornering property, and there are strong interactive effects between the two operating conditions. Therefore, in order to obtain concise expressions, the inflation pressure is incorporated into the UniTire tire model by analogy with the expressions for vertical load, and the interactive effects are also taken into account. Finally, the effectiveness of the improved model is validated by comparison with the experimental data.