A general solution for the stress and displacement of curve cracks distributing along a parabolic curve in an infinite homogeneous anisotropic medium subjected to uniform loading at infinity has been given using the Stroh's formalism and the mapping method. The solutions are valid not only for plane problems, but also for antiplane problems and the problems whose inplane and antiplane deformations couple each other. Explicit solutions for stress intensity factors and crack opening displacement are presented.