Research activities on gigacycle fatigue properties of materials have recently focused on the influence of specimen size used for ultrasonic fatigue tests. In order to increase the volume of material subjected to the maximum stress (risk volume) a new specimen shape with a Gaussian profile is proposed. An approximation of the Gaussian profile with an arc of circle is presented in the paper, in order to simplify the Gaussian specimen manufacturing process. The effect of the approximation is evaluated analytically and through a finite element analysis.