Planetary surface exploration rovers must accurately and efficiently predict their mobility on natural, rough terrain. Most approaches to mobility prediction assume precise a priori knowledge of terrain physical parameters, however in practical scenarios knowledge of terrain parameters contains significant uncertainty. In this paper, a statistical method for mobility prediction that incorporates terrain uncertainty is presented. The proposed method consists of two techniques: a wheeled vehicle model for calculating vehicle dynamic motion and wheel-terrain interaction forces, and a stochastic response surface method (SRSM) for modeling of uncertainty. The proposed method generates a predicted motion path of the rover with confidence ellipses indicating the probable rover position due to uncertainty in terrain physical parameters. Rover orientations and wheel slippage are also predicted. The computational efficiency of SRSM as compared to conventional Monte Carlo methods is shown via numerical simulations. Experimental results of rover travel over sloped terrain in two different uncertain terrains are presented that confirms the utility of the proposed mobility prediction method.