The process industry is moving toward rigorous flowsheet design optimization with modern algorithms. Optimization results are, however, influenced by uncertainty in the parameters of the mathematical models used in the optimization calculation. Parametric uncertainty is typically addressed using scenario-based approaches, whereby the process is optimized for a predetermined, finite set of scenarios representing the statistical properties of the parameters. This paper presents a novel approach for process design under uncertainty. The framework exploits the semi-infinite nature of sequential dynamic optimization, and is based on representing the uncertain parameters as continuous, time-varying disturbance variables acting on a (static) process model over a pseudo-time domain. The parameter uncertainty space is mapped by intersecting, continuous parameter trajectories instead of a limited set of discrete scenarios. We test the proposed strategy on two case studies: a dimethyl ether plant and the Williams-Otto process, demonstrating superior computational performance compared to scenario-based approaches.