A method for computing candidate Attainable Regions (ARs) suitable for implementation on a graphics processing unit (GPU) is discussed. This allows for both fast computation and complex candidate Attainable Regions to be considered. The method is tested on several problems of varying dimension with kinetics that contain multiple steady-states and temperature dependent kinetics. The computation of unbounded regions is also studied. The constructions obtained appear to approximate the AR boundary well and exhibit good convergence in a small number of iteration steps. A brief analysis of the convergence characteristics of the method is also provided and compared to the same algorithm implemented on a conventional multicore central processing unit (CPU). (C) 2014 Elsevier Ltd. All rights reserved.