This paper presents a reliable method of solution of two dimensional shape optimization problems subjected to transient dynamic loads using Genetic Algorithms. Boundary curves undergoing shape changes have been represented by B-splines. Automatic mesh generation and adaptive finite element analysis modules are integrated with Genetic algorithm code to carry out the shape optimization. Both space and time discretization errors are evaluated and appropriate finite element mesh and time step values as obtained iteratively are adopted for accurate dynamic response. Two demonstration problems have been solved, which show convergence to the optimal solution with number of generations. The boundary curve undergoing shape optimization shows smooth shape changes. The combinations of automatic mesh generator with proper boundary definition capabilities, analysis tool with error estimation and Genetic algorithm as optimization engine have been observed to behave as a satisfactory shape optimization environment to deal with real engineering problems.