To Predict the driving force of a cup pig has significant meaning in ensuring the success of its pigging operation. The pigging process of the cup pig with a specific structure under different conditions (with different friction coefficients and interferences) was simulated based on the 3D finite element method (FEM), and the equations of contact stress on cups were studied with the method of nonlinear regression. Additionally, a prediction model of the driving force for cup pig was first established based on the integral form of the contact stress equations. The results indicate that the contact stress equations present two different forms before and after a critical interference which is proved to be related to the cup lip percentage. Besides, the friction coefficient has almost no effect on the distribution of the contact stress while it affects the magnitude of it significantly. The quantitative effect of friction coefficient on the magnitude of contact stress was described by the correction equation which perfects the prediction model, and the extent of the effect is related to the interference. According to the modeling approach introduced in this paper, the driving force of the cup pigs with arbitrary structure forms can also be predicted.