The transportation sector is responsible for 27% of greenhouse gas emissions in the United States, implying that it plays an important role in achieving sustainability goals and slowing down the impact of climate change. To understand the influence of road roughness on vehicle fuel consumption, researchers have recently proposed stochastic pavement models combined with a mechanics-based vehicle model to study the energy dissipated by the vehicle suspension. Solutions were obtained in the frequency domain, where the computational effort increases rapidly as more complicated vehicle types and surface profiles are considered. This paper proposes a new formulation and solution procedure for estimating the energy dissipation in the tire and the suspension of vehicles traversing rough nondeformable pavements. Herein, a filtered white noise model of the road roughness is combined with a quarter-car model of the vehicle to yield an augmented state space representation. The Lyapunov equation governing the covariance of the responses is then solved to obtain the energy dissipation of the vehicle. Subsequently, examples are provided to illustrate the efficacy and flexibility of the proposed approach. (C) 2016 American Society of Civil Engineers.