© 2014 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The aim of this study is to develop analysis and design optimization method for three dimensional nozzles. For analysis, three dimensional Euler equations are solved using both Newton and Newton-GMRES methods and their performances are compared. The Jacobian matrix needed for Newton method is evaluated analytically. Newton-GMRES method is a matrix free solution technique hence it does not require the Jacobian matrix evaluation. For design optimization, only the Newton method is used. A gradient based method is used for numerical optimization. Sensitivities are evaluated by using adjoint method. The objective of the design is to maximize thrust while keeping the mass flow rate constant.