For a specified feed and a specified set of reactions, the attainable region is the set of all reactor network outlet concentrations that can be attained by means of all feasible reactor networks. This work presents a number of novel properties of the reactor network synthesis problem and subsequently of the attainable region. These properties are employed in the development of a so called Shrink-Wrap algorithm that can be used to approximate the true attainable region to any desired level of accuracy. Examples from the literature are used to illustrate the proposed algorithm. (C) 2004 Elsevier Ltd. All rights reserved.