Capacitive Micromachined Ultrasonic Transducers (CMUTs) are an alternative to piezoelectric transducers, offering several potential advantages, including broad bandwidth, mass manufacturability built on standard Micro-Electro-Mechanical Systems (MEMS) processes, and the potential for integration with electronics. Additionally, unlike most piezoelectric transducers, CMUTs are lead-free, addressing recent regulatory pressures regarding the restriction of hazardous substances in medical devices. However, CMUTs have long faced performance and reliability challenges, such as dielectric charging and operational hysteresis. Other factors affecting their performance include poor utilization of real estate, parasitic capacitance, potential for electrical breakdown, premature collapse, ultrasonic welding, and poor electromechanical efficiency when multiple small CMUT cells are used within an element. Recently, our group demonstrated that long rectangular membranes utilizing electrode posts in the cavities not only mitigate many of these reliability issues but also achieve exceptional electromechanical efficiency. In fact, they have exhibited transmit efficiency exceeding that of piezoelectric transducers by nearly threefold. However, these advances lacked a framework for modeling or optimizing this new architecture. One limitation is the absence of an equivalent circuit model for rectangular membranes, partly due to the lack of a method for calculating their radiation impedance. This thesis aims to address this gap. We introduce an approximate model for the radiation impedance of rectangular membranes and validate it against finite element computations. Furthermore, our models have been integrated into equivalent circuit models and tested against both computational results and experimental data.