A method for analyzing capacitive micromachined ultrasonic transducer (CMUT) arrays and arrays of elements composed of several CMUTs is proposed. It is based on a combination of a free acoustic mode description of an isolated CMUT, and the coupling of these modes to the fluid in which waves should be excited or detected through an impedance matrix that will depend on frequency. The parameters of the model describing the isolated CMUT is independent of frequency and excitation of neighbor CMUTs, whereas the acoustic impedance matrix describing the coupling to the fluid will depend on both the excitation of neighbor CMUTs and frequency. Hence, this splitting of the calculations has a potential for saving computer time. The analysis gives transfer functions from excitations that vary harmonically with time and space along the array surface to CMUT parameters as current, mode excitations, or output acoustic pressure. Based on this, the response of essentially arbitrary excitations of the CMUTs may be obtained. The method is used to analyze an infinitely large array of circular CMUTs on a rectangular grid. The CMUTs are assumed to be operating in collapsed mode. Sharp resonances are shown to occur that could be significantly damped by adding series resistors to the CMUTs or increasing the water viscosity.