Answer is yes, at least some of them.
A recently published paper in Applied Physics Letters reveals the posibility to excite and sense shear waves in some plant leaves and use them to get rigidity modulus and Poisson’s ratio.
Unlike animal tissues, plant tissues present a cell wall that provides the tissue and extra rigidity that makes possible the observation of this shear waves at ultrasonic frequencies.
Reference: M. D. Fariñas, D. Sancho-Knapik, J. J. Peguero-Pina, E. Gil-Pelegrín, and T. E. Gómez Álvarez-Arenas, “Shear waves in vegetal tissues at ultrasonic frequencies,” Applied Physics Letters, vol. 102, no. 10, p. 103702, 2013. http://scitation.aip.org/content/aip/journal/apl/102/10/10.1063/1.4795785