A recently developed integral equation method has been used to derive the c
rack opening displacement of an elliptic crack in an infinite elastic mediu
m subjected to a concentrated pair of point force loading at an arbitrary l
ocation on the crack faces. These results have been used to obtain the stre
ss intensity factor along the elliptic crack front which corresponds to the
weight function for an elliptic crack under normal loading. Analytical exp
ression of the weight function can be used to derive the stress intensity f
actor for both polynomial loading as well as non-polynomial loading.