One of the most important applications of sensitivity analysis is gradient computations for optimal design. This paper focuses on the use of Continuous Sensitivity Equation Methods (CSEMs) for shape sensitivity calculations within an optimal design problem. Two methods for computing the shape sensitivities are introduced. The implementations of the methods are very similar; however, the sensitivity approximations obtained from these methods have different convergence properties. Furthermore, gradient approximations computed using each of the sensitivities significantly impact the performance of a trust region algorithm used for parameter identification. This paper includes an overview of the CSEMs and detailed results of the optimization algorithm for each implementation.