A new alternating method for the analysis of a quarter-elliptical corner crack is developed. The completely general analytical solution for an embedded elliptical crack in an infinite solid, subject to arbitrary crack-face tractions, is implemented in the present alternating method. The present finite element alternating method results in an inexpensive procedure for the routine evaluation of accurate stress intensity factors for flawed structural components. The present alternating method is applied to the analyses of various shapes of quarterelliptical corner cracks: 1) in a brick subject to remote tension, 2) emanating from a hole in finite-thickness plates subject to remote tension as well as bearing pressure; and 3) emanating from a pin hole in aircraft attachment lugs subject to simulated pin loading. The results for problems 1 and 2 are compared with those available in literature, for problem 3 the stress intensity factors and their parametric variations for the corner cracks of various shapes are presented.