This book, which is based on the Ph.D. dissertation of Dr. Serkan Dag, presents methods of analysis for the solutions of crack and contact problems in functionally graded materials (FGMs). Among the problems for which new analytical solution procedures are presented are: mixed-mode surface cracking in a graded medium, interaction of a contact stress field with a surface crack and coupled crack and contact problems in graded materials. The first part of the book describes an analytical approach based on the singular integral equations for the analysis of a surface crack located in a homogeneous medium that is loaded through a sliding frictional rigid stamp. The change in the singular behavior of the stress field due to the interaction of the contact zone and the crack mouth is also considered. The following chapters present a new integral equations based technique developed to calculate mixed-mode stress intensity factors for a surface crack located in a graded medium. The book concludes with a chapter that details the integral equations based solution methods for the analysis of coupled crack-contact problems in graded materials.