The operations of a planetary rover depend critically upon the amount of power that can be delivered by its batteries. In order to plan the future operation, it is important to make reliable predictions regarding the end-of-discharge (EOD) time, which can be used to estimate the remaining driving time (RDT) and remaining driving distance (RDD). These quantities are stochastic in nature, not only because there are several sources of uncertainty that affect the rover’s operation but also since the future operating conditions cannot be known precisely. This paper presents a computational methodology to predict these stochastic quantities, based on a model of the rover and its batteries. We utilize a model-based prognostics framework that characterizes and incorporates the various sources of uncertainty into these predictions, thereby assisting operational decision-making. We consider two different types of driving scenarios and develop methods for each to characterize the associated uncertainty. Monte Carlo sampling and the inverse first-order reliability method are used to compute the stochastic predictions of EOD time, RDT, and RDD.