Existing models from scheduling often over-simplify the problems appearing in real-world industrial situations. The original application is often reduced to a single-objective one, where the presence of uncertainty is neglected. In this paper, we focus on multi-objective optimization in uncertain environments. A bi-objective flowshop scheduling problem with uncertain processing times is considered. An indicator-based evolutionary algorithm is proposed to handle these two difficulties (multiple objectives and uncertain environment) at the same time. Four different strategies, based on uncertainty-handling quality indicators, are proposed in the paper. Computational experiments are performed on a large set of instances by considering different scenarios with respect to uncertainty. We show that an uncertainty-handling strategy is a key issue to obtain good-quality solutions, and that the algorithm performance is strongly related to the level of uncertainty over the environmental parameters.