We studied the electromechanical properties of PMN-PT and PZN-PT single crystal plates poled along [001] with thickness t ranging from 800 down to 70 mum. In the case of the tetragonal single domain state (IT), the properties of the thickness mode remain stable down to 250 mum. Below 250 mum, an instability of the polarization is shown. The plates exhibit regions where polarization lies in the plane of the plates. The emergence of these regions results in an additional shear mode at a frequency close to that of the thickness mode, an important increase of the dielectric constants epsivs 33 and epsivT 33 and a decrease of the coupling-factor k1 and longitudinal wave velocity vD 33t. In the rhombohedral multidomain state (4R) a moderate variation of k1 can be observed while epsivs 33 increases with decreasing thickness. The increase of the dielectric constant in the 4R state is also related to an additional shear mode. When / decreases, the volume ratios of each domain family are not equal, leading to a tilt of the average spontaneous polarization away from the poling electric field. Consequently the modification of the domain structure for thin plates leads to a change of the electromechanical properties.