In this paper, two new algorithms for solving a two-stage optimization problem are given. The problem arises during design of chemical processes when there is some uncertainty in original data These algorithms are extensions of an algorithm suggested by Ostrovsky ct al. (1994) [Computers chem. Engng 18(8), 755-767 (1994)]. A distinctive feature of the algorithms is that during an execution of iterations the upper and the lower estimates of the optimal value of an objective function are calculated and the operation of partitioning the uncertainty region is performed. The application of one of the suggested algorithms is illustrated by three examples.