A non-contact method, using photoacoustically generated antisymmetric Lamb waves detected with a laser Doppler technique, is used for determining tension in magnetic tape. For the tape samples used in this study, the bending stiffness contributes as much to the overall stiffness as a 1 Newton tension force, so an accurate determination of the tension must also necessarily include an independent measurement of the bending stiffness. Our data shows that the flexural velocity normal to the direction of the applied tension provides a determination of the bending stiffness independent of tension. The dependence of the wavespeed on tension is measured, showing the expected tension dependence and demonstrating the utility of this approach.