A domain independent integral is obtained from the principle of virtual work. A suitable choice of the virtual displacement field allows variation of the position of a crack tip. For materials possessing a strain energy function Eshelby's definition of the force on a point defect is used to obtain the crack extensioin force. The method is general and allows treatment of a crack whose surfaces and front are curved by unsing curvilinear coordinates. To illustrate the applicability of the method three examples of the point-wise crack extension force are given, with different combinations of crack surface and crack front curvature. A general expression of the crack extension force for curved cracks is suggested. In Cartesian coordinates the proposed expression reduces to the J-integral of Rice.