In materials evaluation applications requiring the interrogation of modified far field patterns of an ultrasonic transducer, it is desirable to use a transducer which produces a beam with a Gaussian profile. A transducer with a velocity profile which is Gaussian as a function of radius and independent of angle is described. The transducer has been constructed by depositing a circularly symmetric metallic multiple electrode array on a 12. 7 mm diameter x-cut quartz disk. Each electrode is independently connected to an impedance network optimized to produce the Gaussian distribution with less than two percent maximum error. A computer aided electrode design and normalized three dimensional ultrasonic measurements of the far field distribution are presented. / Master of Science