Transducers based on piezoelectric crystals dominate the biomedical ultrasonic imaging field. However, fabrication difficulties for piezoelectric transducers limit their usage for complex imaging modalities such as 2D imaging, high frequency imaging, and forward looking intravascular imaging. Capacitive micromachined ultrasonic transducers (CMUTs) have been proposed to overcome these limitations and they offer competitive advantages in terms of bandwidth and dynamic range. Further, the ease of fabrication enables manufacturing of complex array geometries. A CMUT transducer is composed of many electrostatically actuated membranes. Earlier analysis of these devices concentrated on an equivalent circuit approach, which assumed the motion of the membrane was approximated by a parallel plate capacitor. Finite element analysis is required for more accurate results. In this paper, we present the finite element model developed to evaluate the performance of the CMUTs. The model is composed of a membrane radiating into immersion medium. Electrostatic actuation is added on using electromechanical elements. Symmetry boundary conditions are imposed around the sidewalls of the finite element mesh, so that the model reflects the properties of a cell driven with the same phase as its neighboring membranes in an infinitely large array. Absorbing boundaries are implemented one wavelength away from the membrane to avoid reflections from the end of the finite element mesh. Using the model, we optimized the membrane radius, membrane thickness and gap height. Our optimized designed yielded a center frequency of 13 MHz with hundred percent bandwidth. A maximum output pressure of 20 kPascal per volt was obtained.