A system for and a method of measuring ultrasonic wave velocities in a subterranean core specimen is provided. Ultrasonic wave velocities are measured from the side surfaces (faces) of a polygonal-shaped core specimen having at least ten sides or faces. Stress is introduced to the core specimen by hydraulic rams associated with each set of opposing sides. As stress is applied, ultrasonic waves are introduced to at least one side of the set of opposing sides and the wave transmitted through the core specimen is measured. Subsequently, the wave velocity for the ultrasonic wave can be calculated based on the measurements taken. Also, elastic properties associated with the core specimen can be calculated.