This book contains two sections: Chapters 1-7 deal with contact mechanics, and Chapters 8-13 deal with fracture mechanics. The different contributions of this book will cover the various advanced topics of research. It provides some needed background with respect to contact mechanics, fracture mechanics and the use of finite element methods in both. All the covered chapters of this book are of a theoretical and applied nature, suitable for the researchers of engineering, physics, applied mathematics and mechanics with an interest in computer simulation of contact and fracture problems.