The thermal explosion problem of cumene hydroperoxide exothermic reaction which is used in chemical industries for production of some chemical materials is investigated. The analytical solutions of the problem to determine the margin between ignition and non-ignition systems are presented. The solution offers different analytical expressions which relate between the critical parameters for both steady and unsteady-states in different planes of solutions for different cases. The numerical solutions in different planes offer different trajectories of solution as sub-critical (non-ignition) and supercritical (ignition). Also from the numerical solution the relations between the critical parameters are presented. The critical behaviors from both analytical and numerical solutions are concise and pertained the same results. (c) 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.