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Climate change and population growth can affect the supply and the demand sides of transportation networks, respectively. Rational assessment of societal risk of transportation networks should consider these effects, both of which are uncertain in nature. In this paper, a novel method is proposed to assess societal risk of transportation networks subjected to uncertainties due to climate change and future population growth. The method is posited on a robust traffic assignment model using the expected residual minimization approach. A novel algorithm, combining smoothing method, quasi-Newton technique, and Latin hypercube sampling, is developed for the efficient implementation of the proposed method. The proposed method can produce a deterministic traffic flow pattern that deviates as little as possible from the traffic flow patterns associated with all future scenarios. The obtained traffic flow pattern can then be used to estimate societal risk of transportation networks. A number of examples, including a real-world highway bridge network in Camden County, New Jersey, are provided in this paper to demonstrate the efficiency, effectiveness, and application of the proposed method. It is found from the examples that (a) the proposed method is more efficient and robust than existing algorithms for robust traffic assignment under uncertainties, and (b) climate change and population growth can significantly alter the traffic pattern in a transportation network and thus increase the societal risk posed upon traffic users.