In mechanical engineering structural optimization requires an optimized mechanical structure with respect to size and shape. Topology optimization fulfill these requirements. Evolutionary Structural Topology Optimization (ESTO)is key point of this book. Since there was no such ESTO having strong mathematical background. In this book it tries to find and implement such ESTO method in an FEM software. A number of simulations, analysis and parametric study has been performed to ensure about our findings about ESTO method having strong mathematical background.