A method for improving the accuracy of measuring the velocity and time of flight of ultrasonic signals through moving web-like materials such as paper, paperboard and the like, includes a pair of ultrasonic transducers disposed on opposing sides of a moving web-like material. In order to provide acoustical coupling between the transducers and the web-like material, the transducers are disposed in fluid-filled wheels. Errors due to variances in the wheel thicknesses about their circumference which can affect time of flight measurements and ultimately the mechanical property being tested are compensated by averaging the ultrasonic signals for a predetermined number of revolutions. The invention further includes a method for compensating for errors resulting from the digitization of the ultrasonic signals. More particularly, the invention includes a method for eliminating errors known as trigger jitter inherent with digitizing oscilloscopes used to digitize the signals for manipulation by a digital computer. In particular, rather than cross-correlate ultrasonic signals taken during different sample periods as is known in the art in order to determine the time of flight of the ultrasonic signal through the moving web, a pulse echo box is provided to enable cross-correlation of predetermined transmitted ultrasonic signals with predetermined reflected ultrasonic or echo signals during the sample period. By cross-correlating ultrasonic signals in the same sample period, the error associated with trigger jitter is eliminated.