Structures will contain cracks and crack-like flaws before entering into service or will develop them during their service life. It is essential to detect these flaws and quantify their growth so as to enable safety of the structure during its service life. Because of wide application of stress intensity factor approach, many methods, both theoretical and experimental, of evaluating them for various types of cracked configuration have been developed. This thesis deals with a theoretical method of evaluation of S.I.F. for several elliptical crack and punch problems. The thesis is divided into four parts. The first part is concerned with the weight function theory applied to elliptic cracks. The second part deals with the interaction between elliptic cracks. The third part deals with the detection of elliptic crack from the field scattered by it. The fourth and last part considers interaction between elliptic punches. The unique feature of this thesis is that all the problems dealt here reduce to similar type of mixed boundary value problems in the theory of elasticity. All the problems are therefore linked by a single method of solution which is an integral equation method.