This paper considers uncertain constrained systems, and develops two algorithms for computing a probabilistic output admissible (POA) set which is a set of initial states probabilistically assured to satisfy the constraint. The first algorithm is inspired by an existing randomized sequential technique. The second algorithm alleviates the computational effort based on heuristics. The present algorithms terminate in a finite number of iterations and provide a POA set. Additionally, we can obtain information on the size of the resulting set a posteriori. A numerical simulation demonstrates the applicability of the POA set to a control system design scheme. (C) 2007 Elsevier Ltd. All rights reserved.