An improved system for measuring the velocity of ultrasonic signals within the plane of moving web-like materials, such as paper, paperboard and the like. In addition to velocity measurements of ultrasonic signals in the plane of the web in the machine direction, MD, and a cross direction, CD, generally perpendicular to the direction of the traveling web, therefor, one embodiment of the system in accordance with the present invention is also adapted to provide on-line indication of the polar specific stiffness of the moving web. In another embodiment of the invention, the velocity of ultrasonic signals in the plane of the web are measured by way of a plurality of ultrasonic transducers carried by synchronously driven wheels or cylinders, thus eliminating undue transducer wear due to any speed differences between the transducers and the web. In order to provide relatively constant contact force between the transducers and the webs, the transducers are mounted in a sensor housings which include a spring for biasing the transducer radially outwardly. The sensor housings are adapted to be easily and conveniently mounted to the carrier to provide a relatively constant contact force between the transducers and the moving web.