High density tactile sensor arrays based upon ultrasonic pulse- echo ranging will be developed to cover curved surfaces of a dexterous robotic hand. An array of transducers generate ultrasonic pulses which traverse an overlying elastomer sheet and are reflected at its upper surface and return to the transducers. A measurement of the time-of-flight corresponds to the thickness of the sheet. When these sensors are used on a robot end effector to grasp an object, the induced deformation of the sheet is indicated by a change in the time-of-flight. This proposal addresses the problems associated with placing these sensors on curved surfaces on the finger segments and hemispherical finger tips of a dexterous robotic hand. High density arrays with elements 0.5-3 mm square properly distributed on all surfaces will give a mechanical hand near anthropomorphic touch sensing capability.