We have computed the elastic constant tensor for PbZrTiOe, PZT 50/50, in the rhombohedral structure. We find it to be very soft elastically, and the Young's modulus to be very anisotropic. Our results for PZT are compared with literature values on other oxide perovskites, and the new experimental results on PMN-PT and PZN-PT. The elastic response is an important part of the electromechanical re...