Renewable energy (RE) is an important emissions reduction technology for climate change mitigation. Hybrid power systems (HPSs) are designed to facilitate the deployment of RE. This paper addresses HPS design under RE resource uncertainties and presents a two-step mathematical approach. The method involves the use of an optimisation model for HPS sizing and Monte Carlo simulation for results validation. The superstructure-based model considers all feasible power allocation options in an HPS and allows the selection of energy storage technologies. To account for resource uncertainty, chance-constrained programming is applied in the optimisation model and the effective power output of renewable sources can be computed according to the specified system reliability. The optimised HPS configuration is then simulated and its reliability estimated to ensure that the specified system reliability level is achieved. Two case studies of isolated and on-grid HPSs are used to demonstrate the proposed approach. The results show that for higher system reliability, the isolated system requires larger generator and energy storage capacities, whilst the on-grid system requires more grid electricity instead of intermittent RE. Further analyses are performed to explore the trade-off between cost and carbon emissions as well as to assess the effects of electricity price and emission factors on HPS design. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.