The vertical road input is the most important load for durability assessments of vehicles. We focus on stochastic modelling of the road profile with the aim to find a simple by still useful model. The proposed non-stationary Laplace model with ISO spectrum has only two parameters, and can be efficiently estimated from a sequence of roughness indicators, such as IRI or ISO roughness coefficient. Thus, a road profile can be stochastically reconstructed from roughness indicators. Further, explicit approximations for the fatigue damage due to Laplace roads are developed. The usefulness of the proposed Laplace-ISO model is validated for eight measured road profiles. Keywords: Road surface profile, road roughness, road irregularity, Laplace process, non-Gaussian process, power spectral density (PSD), ISO spectrum, roughness coefficient, international roughness index (IRI), vehicle durability, fatigue damage.