In this book, First Fracture analysis has been done for subsurface crack. A Half space model for Subsurface crack has been made and Stress Intensity Factors are obtained.Further the 3D model of Railway Wheel is used to find Fatigue initiation life. A numerical model has been used to Optimize the mass of Railway Wheel by considering geometrical parameters and Fatigue life as variable. The Optimization is run and significant decrease in mass of wheel was obtained.