The generation of ULF waves by ground-based magnetic and electric dipoles is studied with a simplified model consisting of three adjoining homogeneous regions representing the ground, the vacuum (free space) region, and the ionosphere. The system is assumed to be immersed in a homogeneous magnetic field with an arbitrary tilt angle. By the use of Fourier techniques and the method of stationary phase, analytic expressions are obtained for the field strength of the compressional Alfv¿n waves in the ionosphere. Expressions are also obtained for the strength of the torsional Alfv¿n wave in the ionosphere and the ULF magnetic field at ground level. Numerical results are obtained for the compressional Alfv¿n wave field strength in the ionosphere with a nonvertical geomagnetic field and for the ULF magnetic field at ground level for a vertical geomagnetic field.