Impulsively excited ULF waves are studied in the three-dimensional dipole magnetosphere. The properties of coupled compressional and transverse wave fields are found to depend on the longitudinal size of the impulse which is assumed at the magnetopause. The distribution of energy density and the wave spectra are shown for different meridians. We study how compressional waves propagate in the three-dimensional space and excite the corresponding field line resonances, and how the impulse produces ULF waves with many azimuthal wave numberes m. The results suggest that, as the longitudinal width of the impulse becomes larger at the magnetopause, strong field line resonances are likely to be found with the lower m. On the contrary, an impulse which is narrow in longitude may excite the ULF waves with relatively high m. We examine the propagation of both compressional and transverse waves in the azimuthal direction. Our numerical results indicate that transverse waves as well as compressional waves are inclined to have harmonic structures in the azimuthal direction, even though it is well known that the Alfven shear modes become one-dimensional modes along the field lines in the absence of coupling. The structures and coupling of global compressional and toroidal standing waves are also investigated and compared with the previous two-dimensional results. ¿ American Geophysical Union 1991