The objective of this study is to develop a reliable and efficient design tool that can be used in chemically reacting flows. The flow analysis is based on the axisymmetric Euler and the finite rate chemical reaction equations. The finite rate chemistry model includes eight species and eleven reaction equations. These coupled equations are solved by using Newton's method. Both the numerical and the analytical methods are used to calculate the Jacobian matrices. Sensitivities are evaluated by using the adjoint method. The performance of the optimization method is demonstrated for rocket motor nozzle design. (c) 2012 Elsevier Ltd. All rights reserved.