In order to obtain good driving performance,a driving force model is presented for non-pneumatic elastic wheel.Brush model of pneumatic tyres is introduced and the deformations of elastic supports and tread are also taken into account.The longitudinal slip rate is redefined.The grounding pressure distribution of elastic wheels is analyzed and corrected according to speed,temperature and stiffness.Then rolling resistance equation is developed.Finally,simulation is conducted by software CarSim,and the results show that the estimated values are consistent with simulation values,especially at low longitudinal slip rate.The research can help to optimize design of non-pneumatic elastic wheel. In order to obtain good driving performance, a driving force model is presented for non-pneumatic elastic wheel. Brush models of pneumatic tires are introduced and the deformations of elastic supports and tread are also taken into account. The longitudinal slip rate is redefined. grounding pressure distribution of elastic wheels is analyzed and corrected under to speed, temperature and stiffness.Then rolling resistance equation is developed. Finally, simulation is conducted by software CarSim, and the results show that the estimated values ​​are consistent with simulation values, especially at low longitudinal slip rate. the research can help to optimize design of non-pneumatic elastic wheel.