This book presents the design and analysis for development of a Capacitive Micromachined Ultrasonic Transducer (CMUT), a novel sensor and actuator, aimed at replacing the conventional piezoelectric transducers for air-coupled ultrasonic imaging applications. These CMUTs are fabricated using the silicon micromachining technology wherein all fabrication is done on the surface of a silicon wafer by means of thin-film depositions, patterning with photolithography and etching. The main emphasis of this study is on developing analytical models that serve as effective design tools for the development of these devices. A desirable goal this manuscript is to create reasonable mathematical models, obtain analytical solutions, wherever possible, for various measures of transducer performance and provide design aids.