In this paper, the problems of composite-patch repair of (i) center and edge-cracked panels loaded in the far-field; and (ii) cracks emanating from pin-loaded fastener holes, are examined in thorough detail. The effects of various non-dimensional design parameters on the reduction in the stress-intensity factors near the crack-tip are determined, and are presented in the form of design charts. Both analytical and numerical methods are employed in this study. In the analytical method, the cracked metallic plate was considered to be infinitely large, and the composite patch was modeled as a long orthotropic strip of finite height (in the direction perpendicular to the crack axis). Next, by using the Finite Element Alternating Method (FEAM), a more general analysis capability that can treat arbitrary shapes of the cracked metallic sheet, as well as of the composite patches, is developed. This general FEAM is applied to: (i) composite patch repairs of cracks emanating from loaded fastener holes (the MSD problem); (ii) composite patch repairs of semi-elliptical surface flaws in thick plates; and (iii) composite patch repairs of quarter-elliptical surface flaws emanating from fastener holes. Problem (i) is two-dimensional in nature while problems (ii) and (iii) are fully three-dimensional. In all these cases, the effects of various design parameters on the crack-tip (front) stress-intensity factors are fully discussed.