Using the dipole magnetic field model, we have developed the theory of field line resonances of hydromagnetic Alfv¿n waves in general magnetic field geometries. In this model, the Alfv¿n speed thus varies both perpendicular and parallel to the magnetic field. Specifically, it is found that field line resonances do persist in the dipole model. The corresponding singular solutions near the resonant field lines as well as the natural definition of standing shear Alfv¿n eigenfunctions have also been systematically derived. ¿ American Geophysical Union 1989