This book is written from the research work carried out for Doctoral research studies of Dr.G.Narayana Naik at the Indian Institute of Science, Bangalore, India. The composite materials has been widely used in all fields of Engineering such as Aerospace, Automobile, Civil, Mechanical, Chemical, Electrical, Electronics, Medical, Nanotechnology, Biotechnology etc. The failure in a composite is a complex process because failure is mainly based on the initiating failure mechanisms. No single failure criterion predicts all the initiating failure mechanisms in a composite subjected to loadings. Hence, development of new failure criterion called the “Failure Mechanism Based Failure Criterion” is presented in this book. Additionally, design optimization of composite structures using nature inspired optimization techniques such as Genetic Algorithms and Particle Swarm Optimization are presented in this book. This book deals about the comparison of different failure criteria, development of new failure criterion, design optimization of composites. Hence, this book will be useful for graduate students, researchers, practising professionals, faculties etc.