This paper presents the simulation and optimal design of an auto-thermal ammonia synthesis reactor. The main objective in the optimal design of an auto-thermal ammonia synthesis reactor is the estimation of optimal length of reactor for different top temperatures with the constraints of energy and mass balance of reaction and feed gas temperature and mass flow rate of nitrogen for ammonia production. Thousands of combinations of feed gas temperature, nitrogen mass flow rate, reacting gas temperature and reactor length are possible. In the present study, NAG subroutine (D02EJF) in MATLAB (with analytical Jacobian) for simulation in combination with Quasi-Newton (QN) method for optimization is used to verify the contradictory results reported using gear package of old NAG subroutine (D02EBF), which is now replaced with D02EJF, in combination with simple GA in earlier literature. And the new NAG subroutine shows a unimodal characteristic of the objective function, compared to a multimodal one found in the past study. It is found that new routine (D02EJF) neither showed any spikes, reverse reaction effect nor the equation became unstable even at a high top temperature of 800 K. New results are obtained for reactor length and optimal cost of reactor. (c) 2004 Elsevier Ltd. All rights reserved.