A method based upon simple diffraction theory is described for the calculation of modified paraboloid reflectors to produce from a point source a shaped beam of arbitrary shape in one plane and uniformly narrow in the perpendicular planes. A specific application of the shaped beam antennas is in connection with radar antennas designed for height finding. In this case the antenna must have a sharp elevation beam for obtaining precise elevation information and a rapid elevation scan. The beam must be relatively broad in azimuth in order that the target will be held in the beam long enough to obtain height information. If a fixed minimum of illumination is to be achieved at a given linear distance on both sides of the center line of the azimuth beam, the amplitude pattern must have the so-called “double cosecant” or “beavertail' shape.