The magnetization-curling mode in a columnar-structure film with perpendicular magnetization is studied on the assumption that the film is a two-dimensional array of cylinders. The angular dependence of the nucleation fieldHNis calculated by the Ritz method and compared with that for the coherent-rotation mode. It is found that the magnetization rotates in the curling mode for a large reduced radiusSand in the coherent-rotation mode for a smallS.The angular dependence ofHNis different from that in an infinite cylinder. IfSis large, the magnetization rotates in the curling mode for any value of&thgr;0,where&thgr;0is the angle between the applied field and the cylinder axis. WhenSis medium, the magnetization rotates in the coherent-rotation mode for a small&thgr;0and in the curling mode for a large&thgr;0.©1997 American Institute of Physics.