In this investigation, an exact three-dimensional weight function is developed for the elliptical crack family. Closed form expressions for the weight function of the penny-shaped and elliptical crack in an infinite body subjected to symmetric applied stresses are obtained. Several loadings are considered that lead to exact solutions which agree with those in the literature. Since crack-opening displacements for more complicated crack geometries do not appear in the literature, an approximate weight function is proposed. When applied to the geometries with known solutions, excellent agreement is obtained. When employed to determine the stress-intensity factor for a semielliptical and quarter-elliptical crack in a plate subjected to bending stresses, it produces results which are good for short cracks.